Rangers overcame a stiff challenge by Motherwell to keep the pressure on Scottish Premier League leaders Celtic.
Boyd grabbed the third goal to secure Rangers' victory
A Carlos Cuellar header had already struck the Motherwell crossbar by the time Daniel Cousin's low drive found the net after 42 minutes.
But Well dominated after the break and Paul Quinn headed home from close range after a 65th-minute corner.
However, Chris Porter headed into his own net five minutes later and Kris Boyd slotted home a late third.
Motherwell boss Mark McGhee had named an unchanged side despite their surprise 3-0 defeat at home to Falkirk.
Chris Burke came in for the suspended Lee McCulloch as Rangers manager Walter Smith stuck by the side that played so well in drawing with Aberdeen despite being down to 10 men.
The winger looked determined to make an impression in only his third appearance of the season as he curled a drive just over from 18 yards after a superb burst from the halfway line.
Rangers' Allan McGregor was tested when Steve McGarry's cross found the diving head of Ross McCormack 10 yards out and the ball bounced clear off the goalkeeper's knees.
Burke again threatened with a low curler that goalkeeper Graeme Smith did well to turn round the post.
The goalkeeper was well beaten when Cuellar's header crashed off the underside of the bar from the resulting corner and Steven Naismith turned the rebound wide from four yards.
Motherwell felt hard done-by when Rangers took the lead after 42 minutes.
The visitors thought they had won a corner, but Rangers broke clear and, after a superb move, a deflected effort from Barry Ferguson was cleared off the line by Stephen Craigen.
Quinn gave Motherwell a deserved equaliser after the break
But the pressure was still on and Steven Whittaker's low cross was driven into the far corner by Cousin from 16 yards.
Motherwell came out fighting after the break and McCormack came close twice to equalising.
First, he tried to square the ball instead of going for goal from 12 yards, and when found again in a similar position, he fired against the legs of McGregor.
David Clarkson should have done better than head over from 10 yards and the striker was then thwarted by a fine Alan Hutton tackle after a low McCormack cross into the six-yard box.
Thomas Buffel, returning from a long injury absence, replaced the tiring Naismith for Rangers, while Motherwell introduced Darren Smith in place of McGarry.
But, before either sub had a chance to have a touch on the ball, Quinn headed home from 10 yards following a corner.
Rangers' response was immediate and Cousin sent a header against the crossbar from a Burke cross.
The lead was restored when Charlie Adam's corner was headed into his own net by Porter.
And Hutton fired over after a superb run into the penalty box before substitute Boyd added the third in stoppage time.
Rangers: McGregor, Hutton, Cuellar, Weir, Whittaker, Burke, Ferguson, Thomson, Adam, Naismith (Buffel 64), Cousin (Boyd 75).
Subs Not Used: Carroll, Ehiogu, Hemdani, Lennon, Furman.
Goals: Cousin 42, Porter 70 og, Boyd 90.
Motherwell: Graeme Smith, Quinn, Craigan, Reynolds, Paterson, McGarry (Darren Smith 64), Hughes, O'Donnell, McCormack, Porter, Clarkson (Murphy 83).
Subs Not Used: Meldrum, Corrigan, Brian McLean, Lasley, Fitzpatrick.
Booked: Craigan, O'Donnell, Paterson.
Goals: Quinn 65.
Ref: S Conroy