Despite his side failing to score in their last four league games, Coyle kept faith with his misfiring attack, while Allardyce brought 19-year-old Hoilett in for Brett Emerton.
Rovers, playing their first game in 11 days, began with a spring in their step and had the ball in the net after six minutes, but Morten Gamst Pedersen's long throw-in did not touch anyone before it sailed over keeper Jussi Jaaskelainen's head.
During the course of the first half, Bolton's Premier League goalscoring drought passed the seven-hour mark and Fabrice Muamba summed up their recent struggles when he curled a shot over from a good position.
But the midfielder more than made up for it when he blocked Keith Andrews' header on the line, and then diverted Kalinic's follow-up onto the post.
Bolton worked a good opening after 41 minutes, Chung-Yong Lee's cross reaching Matt Taylor at the far post only for Paul Robinson to block the shot.
Two minutes later, however, the visitors were behind as Hoilett's crossfield ball left Blackburn with a two-on-one, which led to Pedersen nodding down for Kalinic to run on and slot in via Knight's desperate block.
Allardyce hails 'best win of the season'
The second half became a battle of the keepers in increasingly difficult conditions as the heavy snow made visibility almost impossible.
Robinson dived bravely at the feet of Ricardo Gardner, but Jaaskelainen bettered that moments later when he kept out Hoilett's header after the young midfielder had laid the ball off to Pedersen and burst into the box to meet the resulting cross.
Jaaskelainen made his best save of the match by clawing Steven Nzonzi's header from under the bar, but that was soon forgotten when Blackburn scored their second from the resulting corner.
Bolton's defence again fell apart, allowing Givet to hook the half-cleared corner back in for Roberts to slot the ball under Jaaskelainen's body.
Givet completed a poor day for Bolton's defence - missing long-term injury victim Gary Cahill - when he rose highest to get the slightest of touches onto El Hadji Diouf's cross.
Rovers almost scored a fourth when Kalinic and Diouf narrowly failed to get a vital touch on Pedersen's dangerous ball across the box.
A 4-0 defeat would have been harsh on Bolton, but with his defence creaking and his strikers continuing to struggle, Coyle will have left Ewood Park with plenty to think about.
Blackburn boss Sam Allardyce: "It was a fantastic day for us and a very important three points.
"It's our biggest win of the season. We're making everyone sit up and think what a game they're going to get here - and they certainly are.
"The second goal knocked the stuffing out of Bolton and we just opened them up if and when we saw fit."
Bolton boss Owen Coyle: "It's no excuse to say you've played a lot of games, we still expect better that what we offered today.
"I think there was a 20-minute period at the start of the second half where we looked like ourselves and could have had an equaliser.
"The goals we lost, I wouldn't expect to lose those in the school playground. That was really disappointing."
90:00+3:39 The referee blows for the end of the match.
90:00+2:40 Mark Davies concedes a free kick for a foul on El-Hadji Diouf. El-Hadji Diouf restarts play with the free kick.
89:16 El-Hadji Diouf decides to take the corner short.
88:31 Short corner taken by David Dunn from the left by-line.
88:07 Zat Knight sends in a cross, save by Paul Robinson.
86:25 Gretar Rafn Steinsson restarts play with the free kick.
86:25 Substitution David Dunn is brought on as a substitute for Nikola Kalinic.
86:25 Unfair challenge on Kevin Davies by Gael Givet results in a free kick.
85:59 Ivan Klasnic takes a shot. Paul Robinson makes a save.
83:51 El-Hadji Diouf provided the assist for the goal.
83:51 GOAL - Gael Givet:Blackburn 3 - 0 Bolton Gael Givet grabs a headed goal from deep inside the penalty area. Blackburn 3-0 Bolton.
83:51 The ball is crossed by El-Hadji Diouf,
83:17 Foul by Gretar Rafn Steinsson on Jason Roberts, free kick awarded. Morten Gamst Pedersen restarts play with the free kick.
82:32 The ball is delivered by Gretar Rafn Steinsson, Kevin Davies has an effort at goal from the edge of the box that misses to
the right of the target.
80:54 Free kick awarded for a foul by Michel Salgado on Mark Davies. Paul Robinson takes the free kick.
79:34 Free kick awarded for an unfair challenge on Ivan Klasnic by Vincenzo Grella. Vladimir Weiss crosses the ball in from the
78:36 Foul by Jason Roberts on Vladimir Weiss, free kick awarded. The free kick is swung in left-footed by Paul Robinson, clearance
by Steven Nzonzi.
77:02 Effort on goal by Nikola Kalinic from deep inside the area goes harmlessly over the bar.
74:26 Free kick crossed right-footed by Morten Gamst Pedersen.
74:26 Booking Gretar Rafn Steinsson goes into the referee's book for unsporting behaviour.
74:23 Foul by Gretar Rafn Steinsson on Nikola Kalinic, free kick awarded.
Correction - 72:44 Gael Givet provided the assist for the goal.
72:44 Assist on the goal came from Gael Givet.
72:44 GOAL - Jason Roberts:Blackburn 2 - 0 Bolton Jason Roberts gets on the score sheet with a goal from inside the penalty area to the bottom right corner of the goal. Blackburn
72:24 Inswinging corner taken by Morten Gamst Pedersen from the left by-line.
71:28 Inswinging corner taken by Morten Gamst Pedersen, Steven Nzonzi takes a shot. Jussi Jaaskelainen makes a save.
70:24 Nikola Kalinic challenges Ricardo Gardner unfairly and gives away a free kick. Paul Robinson takes the direct free kick.
70:12 Ivan Klasnic takes a shot. Paul Robinson makes a save.
69:10 Free kick awarded for a foul by Vincenzo Grella on Kevin Davies. Ricardo Gardner takes the free kick.
68:10 Substitution Ivan Klasnic replaces Johan Elmander.
66:10 Unfair challenge on Johan Elmander by Steven Nzonzi results in a free kick. Ricardo Gardner crosses the ball in from the free
kick, clearance by Gael Givet.
64:40 El-Hadji Diouf fouled by Mark Davies, the ref awards a free kick. Morten Gamst Pedersen crosses the ball from the free kick
left-footed from left channel, save by Jussi Jaaskelainen.
63:26 Free kick awarded for a foul by Morten Gamst Pedersen on Gretar Rafn Steinsson. Free kick crossed by Ricardo Gardner, clearance
by Keith Andrews.
62:24 Mark Davies takes a shot. Blocked by Steven Nzonzi.
62:05 Short corner taken by Vladimir Weiss.
60:36 Vladimir Weiss decides to take the corner short.
59:36 Indirect free kick taken by Jussi Jaaskelainen.
59:36 Substitution Jason Roberts comes on in place of David Hoilett.
59:36 Nikola Kalinic is caught offside.
58:31 Substitution Matthew Taylor leaves the field to be replaced by Vladimir Weiss.
58:31 Substitution Mark Davies comes on in place of Fabrice Muamba.
57:35 Chung-Yong Lee takes a shot. Paul Robinson makes a save.
56:11 Paul Robinson concedes a free kick for a foul on David Hoilett. Morten Gamst Pedersen crosses the ball, Header from close
in by Nikola Kalinic misses to the left of the target.
54:20 The referee gives a free kick against Nikola Kalinic for handball. Free kick taken by Jussi Jaaskelainen.
53:19 Inswinging corner taken left-footed by Morten Gamst Pedersen from the right by-line, save by Jussi Jaaskelainen.
53:05 Nikola Kalinic takes a shot. Paul Robinson gets a block in.
51:09 The ball is delivered by Morten Gamst Pedersen, David Hoilett takes a shot. Save by Jussi Jaaskelainen. Outswinging corner
taken from the left by-line by Morten Gamst Pedersen, Ricardo Gardner makes a clearance. Gael Givet challenges Jussi Jaaskelainen
unfairly and gives away a free kick. Jussi Jaaskelainen takes the free kick.
45:01 The second half begins.
45:00+2:36 The players leave the pitch at half time.
45:00+1:49 Matthew Taylor takes a shot. Blocked by Martin Olsson.
45:00+0:52 The official flags El-Hadji Diouf offside. Free kick taken by Jussi Jaaskelainen.
45:00+0:22 Chung-Yong Lee gives away a free kick for an unfair challenge on El-Hadji Diouf. Paul Robinson takes the free kick.
42:41 Unfair challenge on Gretar Rafn Steinsson by Nikola Kalinic results in a free kick. Gretar Rafn Steinsson takes the direct
40:56 Morten Gamst Pedersen provided the assist for the goal.
40:56 GOAL - Nikola Kalinic:Blackburn 1 - 0 Bolton Goal scored by Nikola Kalinic from just inside the penalty area to the bottom right corner of the goal. Blackburn 1-0 Bolton.
40:12 Matthew Taylor takes a shot. Save by Paul Robinson.
37:42 Jussi Jaaskelainen takes the indirect free kick.
37:42 Substitution Vincenzo Grella joins the action as a substitute, replacing Ryan Nelsen.
37:42 El-Hadji Diouf is ruled offside.
37:09 The ball is delivered by Morten Gamst Pedersen, Jussi Jaaskelainen makes a save.
35:53 Morten Gamst Pedersen takes the inswinging corner, save made by Jussi Jaaskelainen.
35:00 Johan Elmander challenges David Hoilett unfairly and gives away a free kick. Paul Robinson takes the free kick.
31:03 Unfair challenge on Nikola Kalinic by Paul Robinson results in a free kick. Direct effort from the free kick comes in from
Morten Gamst Pedersen.
30:34 Free kick awarded for an unfair challenge on Paul Robinson by David Hoilett. Free kick taken by Jussi Jaaskelainen.
28:29 The referee blows for offside. Paul Robinson restarts play with the free kick.
27:11 Morten Gamst Pedersen concedes a free kick for a foul on Fabrice Muamba. Free kick taken by Gretar Rafn Steinsson.
25:34 Foul by David Hoilett on Kevin Davies, free kick awarded. The free kick is swung in left-footed by Matthew Taylor.
20:16 Inswinging corner taken left-footed by Morten Gamst Pedersen played to the near post, Ryan Nelsen takes a shot. Fabrice Muamba
manages to make a clearance. Shot by Nikola Kalinic from deep inside the box hits the post.
19:07 Unfair challenge on Chung-Yong Lee by David Hoilett results in a free kick. Jussi Jaaskelainen restarts play with the free
18:22 The assistant referee signals for offside against Kevin Davies. Paul Robinson takes the free kick.
16:19 Free kick awarded for a foul by Fabrice Muamba on Morten Gamst Pedersen. Morten Gamst Pedersen crosses the ball from the free
kick left-footed from left wing, Zat Knight gets a block in.
14:45 Shot from just outside the box by Fabrice Muamba goes over the bar.
13:24 Samuel Ricketts gives away a free kick for an unfair challenge on Nikola Kalinic. Morten Gamst Pedersen delivers the ball
from the free kick left-footed from right channel, Jussi Jaaskelainen makes a save.
11:19 Kevin Davies takes a shot. Blocked by Michel Salgado.
10:17 Free kick awarded for a foul by Matthew Taylor on Michel Salgado. Paul Robinson takes the free kick.
9:08 Chung-Yong Lee takes the inswinging corner, clearance by Keith Andrews.
9:02 The ball is sent over by Matthew Taylor, clearance made by Gael Givet.
8:48 The ball is delivered by Matthew Taylor, clearance made by Ryan Nelsen.
7:33 The referee blows for offside against Nikola Kalinic. Jussi Jaaskelainen takes the free kick.
6:57 Nikola Kalinic fouled by Zat Knight, the ref awards a free kick. Free kick crossed left-footed by Morten Gamst Pedersen.
6:29 Morten Gamst Pedersen has an effort at goal from outside the box missing to the wide left of the goal.
5:00 Fabrice Muamba produces a right-footed shot from outside the penalty area and misses left.
1:45 David Hoilett gives away a free kick for an unfair challenge on Jussi Jaaskelainen. Direct free kick taken by Jussi Jaaskelainen.
0:00 The game begins.
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