Boyd (centre) scored Rangers' second goal at Ibrox
Unconvincing Rangers overcame some nervous moments before goals from Jean-Claude Darcheville and Kris Boyd ensured victory over Aberdeen.
The Dons' Derek Young had been denied by a fine Allan McGregor save during an even first half.
Opposite number Jamie Langfield prevented a Lee Mair own goal.
But Darcheville forced the ball home from close range and, after Pedro Mendes cleared off Rangers' line, Boyd settled the game with a neat header.
It meant that Rangers remain four points behind Scottish Premier League leaders Celtic, who had put the pressure on with victory over St Mirren in the day's early kick-off.
Rangers could have taken the lead within a couple of minutes when Boyd blasted over from a tight angle after being picked out superbly by Mendes.
Injuries to Kenny Miller and Steven Davis meant starts for Darcheville and Kyle Lafferty up front for Rangers.
With Sasa Papac and Madjid Bougherra still missing through injury injury, manager Walter Smith continued to experiment with striker Lee McCulloch in defence.
And there were early moments of panic at the back as Aberdeen pushed forward.
However, there was controversy at the other end when Andrew Considine played the ball against his own hand as he tried to clear a Charlie Adam drive before hastily booting the ball upfield.
Referee Craig Thomson waved away the claims for a penalty, but that and a long-range curling effort from Boyd were rare moments of danger for an Aberdeen who had started without the injured Darren Mackie.
Adam was fortunate that a late stamp on Sone Aluko's ankle was missed by the officials after the midfielder had cleared his lines.
It was the home support's turn to be incensed when Thomson blew his whistle for a head knock suffered by Derek Young as Barry Ferguson continued the play by slotting the ball into the net from 22 yards.
Darcheville opened the scoring against Aberdeen
The two best efforts of the first half came in the dying seconds.
A Young drive forced a fine save from Allan McGregor, whose opposite number, Langfield, then did well to tip the ball over the bar after an Adam free-kick was steered towards the underside of the crossbar off the head of Dons defender Lee Mair.
Rangers had laboured against an Aberdeen side in which Charlie Mulgrew, Gary McDonald and Mair had replaced Richard Foster, Jared Hodgkiss and Darren Mackie.
But Dons boss Jimmy Calderwood's tactics were undone when the Dons failed to clear an Adam corner, Darcheville forcing the ball home from four yards after the ball had been prodded forward by first Kirk Broadfoot then Boyd.
Mendes headed off his own line when Zander Diamond's effort looked destined for an equaliser.
And, with Boyd poised to be replaced with DaMarcus Beasley, the striker sent a cheeky header into the net after Lafferty had stepped over another dangerous Adam corner.
Rangers manager Walter Smith: "It was a good game, a close game. Aberdeen had a lot of set-pieces, long throws played into the box and they were dangerous in that respect.
"In the second half of the game, we started to impose ourselves and obviously we were delighted when we managed to get the breakthrough. I felt with the second half performance that we deserved to shade it.
"But, credit to Aberdeen, it was a good first half from them and, with all the changes in our side, we took a while to settle.
"We lost four players who've been playing regularly for us - Sasa Papac, Majdid Bougherra, Kenny Miller and Steve Davis - and that little bit of disruption meant we weren't as cohesive as usual."
Aberdeen manager Jimmy Calderwood: "I thought we dominated the first 45 minutes. We didn't create too many chances, but we were causing massive problems and they weren't causing us too many problems at all.
"Rangers had a problem with our passing, culminating with a great chance for wee Derek and Allan McGregor has made a wonderful save just before half-time.
"I think, if we'd gone 1-0 ahead at that moment, with the Rangers fans getting a bit restless, well...
"The first goal is so important and both goals Rangers got were scruffy, from two corners, three yards from goals - it's hurting us big time."
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