However, few could deny that the Croatian champions - knocked out of Champions League qualifying by Red Bull Salzburg - were well worth their victory.
Hearts manager Csaba Laszlo set out a cautious line-up against a team who had scored 21 goals in four Croatian league matches.
Laszlo admits to gulf in quality
Christian Nade cut a lonely figure up front as the Edinburgh side allowed Dinamo to play the ball about in front of them.
But the approach was quickly undone as, with less than five minutes on the clock, Hearts found themselves behind.
Dinamo's Brazilian midfielder Sammir turned Jose Goncalves in the left-back area with a shimmy of the hips before sending a deep cross to the back post.
Hearts goalkeeper Marian Kello was caught underneath the ball and Mandzukic rose to head in from a couple of yards.
The goal spurred the home side on to dominate with some neat passing exchanges, and it was only when Dinamo were forced into an early change on 20 minutes that the Hearts players could get some relief and take on fluids in the hot and humid conditions.
Mandzukic opened the scoring within five minutes
But the respite was brief, and Kello saved headers from Mandzukic and Papadopoulos before, rooted to the spot, he watched Perdo Morales' long-range strike batter the bar on the way over.
With Hearts struggling to get on the ball and make any impact, Greek striker Papadopoulos doubled the Croatian side's advantage 10 minutes before half-time, side-footing into the empty net after Kello had parried Sammir's shot.
Five minutes into the second period Suso made Dinamo keeper Tomislav Butina save from a low drive after good work from substitute Ian Black.
Hearts had the newly-laid pitch to thank for not going further behind, when Mandzukic slipped as he pulled the trigger inside the box.
But shortly afterwards it was 3-0, when a lightning Dinamo break up-field culminated in Vrdoljak side-stepping Eggert Jonsson to curl a right-footed effort inside the post from 18 yards.
Then, with just an hour gone, former Liverpool defender Biscan rose free at a corner to head the fourth from a corner.
The scoreline could have been even heavier had it not been for Kello who made a number of additional saves.
Live text and stats
Thursday, 20 August 2009
Europa League Q'fying
07 Etto (Tomecak 20)
10 Sammir (Kramaric 61)
77 Morales (Calello 76)
05 Jose Goncalves
21 Ismael Bouzid (Black 46)
26 Zaliukas yellow card
07 Suso Santana (Novikovas 81)
14 Nade yellow card (Glen 58)
Ref: IvanovAtt: 22,000
Attempts on target
Attempts off target
90:00+3:31 The final whistle is blown by the referee.
90:00+3:01 Corner taken by Arvydas Novikovas from the left by-line, clearance made by Ivica Vrdoljak.
89:16 Shot from just outside the box by Milan Badelj misses to the left of the goal.
88:25 Mario Mandzukic delivers the ball, Lee Wallace makes a clearance.
87:12 Foul by Ivica Vrdoljak on Eggert Jonsson, free kick awarded. Eggert Jonsson takes the free kick.
85:40 Ivan Tomecak produces a cross, Dimitrios Papadopoulos has an effort at goal from close in that hits the post.
85:02 Short corner taken by David Obua.
84:21 Ivan Tomecak challenges David Obua unfairly and gives away a free kick. Free kick crossed by David Obua, clearance by Ivica
80:26 Substitution Arvydas Novikovas replaces Suso Santana.
77:35 Andrej Kramaric fouled by Lee Wallace, the ref awards a free kick. Free kick crossed by Milan Badelj, Lee Wallace manages
to make a clearance.
76:39 Ruben Palazuelos challenges Mario Mandzukic unfairly and gives away a free kick. Milan Badelj crosses the ball in from the
free kick, Lee Wallace makes a clearance.
75:18 Substitution Pedro Morales leaves the field to be replaced by Adrian Calello.
74:34 The assistant referee flags for offside against Ian Black. Tomislav Butina restarts play with the free kick.
74:21 Free kick awarded for an unfair challenge on Jose Goncalves by Andrej Kramaric. Jose Goncalves takes the free kick.
72:56 Eggert Jonsson produces a cross, clearance made by Ivan Tomecak.
71:30 Gary Glen challenges Tomislav Barbaric unfairly and gives away a free kick. Tomislav Butina takes the free kick.
69:41 Foul by Ian Black on Ivica Vrdoljak, free kick awarded. Igor Biscan restarts play with the free kick.
68:42 Dimitrios Papadopoulos takes a shot. Blocked by Lee Wallace.
65:45 Free kick awarded for a foul by Eggert Jonsson on Mario Mandzukic. Milan Badelj restarts play with the free kick.
65:11 Booking Booking for Marius Zaliukas for dissent.
64:45 The referee blows for offside against Dimitrios Papadopoulos. Marian Kello takes the indirect free kick.
64:03 Corner taken right-footed by Pedro Morales, clearance by Lee Wallace.
60:51 Substitution Andrej Kramaric replaces Jorge Sammir.
59:19 Assist by Pedro Morales.
59:19 GOAL - Igor Biscan:Dinamo Zagreb 4 - 0 Hearts Igor Biscan grabs a headed goal from close range. Dinamo Zagreb 4-0 Hearts.
58:42 Inswinging corner taken right-footed by Pedro Morales from the right by-line to the near post,
57:42 Dimitrios Papadopoulos produces a curled right-footed shot from 18 yards. Marian Kello makes a save.
57:08 Substitution Gary Glen comes on in place of Christian Nade.
55:31 GOAL - Ivica Vrdoljak:Dinamo Zagreb 3 - 0 Hearts Ivica Vrdoljak finds the net with a goal from a long way out to the bottom right corner of the goal. Dinamo Zagreb 3-0 Hearts.
54:56 The offside flag is raised against Mario Mandzukic. Jose Goncalves takes the indirect free kick.
54:00 Mario Mandzukic produces a left-footed shot from deep inside the penalty box which goes wide of the left-hand upright.
52:01 Ivan Tomecak produces a right-footed shot from deep inside the penalty area which goes wide of the right-hand post.
50:30 Inswinging corner taken right-footed by Suso Santana from the right by-line, Headed effort from the edge of the area by Jose
Goncalves goes wide of the right-hand post.
48:48 Pedro Morales produces a right-footed shot from just outside the penalty box that misses to the left of the target.
45:27 Jorge Sammir gives away a free kick for an unfair challenge on Lee Wallace. Marian Kello takes the indirect free kick.
45:27 Substitution Ian Black on for Ismael Bouzid.
45:01 The referee gets the second half underway.
45:00+1:01 The ref blows to end the first period.
44:51 Booking The referee shows Christian Nade a yellow card.
42:04 Foul by Santos Carlos on Suso Santana, free kick awarded. Suso Santana delivers the ball from the free kick right-footed
from right wing, clearance made by Tomislav Barbaric.
40:37 Mario Mandzukic produces a right-footed shot from just outside the penalty box that misses to the left of the goal.
Correction - 38:58 Unfair challenge on Dimitrios Papadopoulos by Ismael Bouzid results in a free kick. Pedro Morales shoots direct from the free
38:58 Unfair challenge on Dimitrios Papadopoulos by Ismael Bouzid results in a free kick. Pedro Morales fires a strike on goal direct
from the free kick.
35:47 GOAL - Dimitrios Papadopoulos:Dinamo Zagreb 2 - 0 Hearts Dimitrios Papadopoulos fires in a goal from inside the penalty box to the bottom right corner of the goal. Dinamo Zagreb 2-0
Correction - 35:21 The ball is sent over by Mario Mandzukic, Ivica Vrdoljak takes a shot. Save by Marian Kello.
35:21 Mario Mandzukic delivers the ball, Ivica Vrdoljak takes a shot. Marian Kello makes a save.
34:10 Free kick awarded for a foul by Ismael Bouzid on Jorge Sammir. Pedro Morales produces a strike on goal direct from the free
kick, save by Marian Kello.
31:20 Short corner worked by Pedro Morales, Dimitrios Papadopoulos takes a shot. Marian Kello makes a save.
29:50 Santos Carlos concedes a free kick for a foul on Suso Santana. The free kick is swung in right-footed by Suso Santana, Igor
Biscan manages to make a clearance.
26:03 Corner from the right by-line taken by Ivan Tomecak, Jorge Sammir takes a shot. Ismael Bouzid gets a block in.
21:52 Pedro Morales takes a shot.
20:39 Corner from the right by-line taken by Jorge Sammir, Mario Mandzukic takes a shot. Save by Marian Kello.
20:11 Milan Badelj produces a cross, Dimitrios Papadopoulos takes a shot. Blocked by Marian Kello.
19:17 Substitution (Dinamo Zagreb) makes a substitution, with Ivan Tomecak coming on for Oeliton Etto.
13:50 Inswinging corner taken from the left by-line by Pedro Morales, clearance made by David Obua.
13:07 Corner taken right-footed by Mario Mandzukic, clearance by David Obua.
10:29 Dimitrios Papadopoulos is ruled offside. Marian Kello restarts play with the free kick.
8:49 Jorge Sammir takes a shot from inside the box clearing the bar.
5:00 The assist for the goal came from Jorge Sammir.
5:00 GOAL - Mario Mandzukic:Dinamo Zagreb 1 - 0 Hearts Mario Mandzukic finds the net with a headed goal from close range. Dinamo Zagreb 1-0 Hearts.
4:53 The ball is sent over by Jorge Sammir,
Correction - 1:47 Free kick awarded for an unfair challenge on Jorge Sammir by Lee Wallace. Direct effort from the free kick comes in from
1:47 Free kick awarded for a foul by Lee Wallace on Tomislav Barbaric. Shot comes in from Pedro Morales from the free kick.
0:00 The match has kicked off.
Live text and data provided by The Press Association.
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