Rabbi Matondo’s early goal was cancelled out by a Bojan Moivski effort on the stroke of half-time, before Todd Cantwell marked his 50th competitive appearance with a match winning strike in the second-half.
From the 3-0 victory over Livingston, Philippe Clement named four changes to his side as John Souttar, Ridvan, Tom Lawrence and Cyriel Dessers came into the starting line-up in place of Leon Balogun, Borna Barisic, Ryan Jack and Fabio Silva.
Balogun was out of the matchday squad after a head knock at the weekend, while the manager confirmed Ryan Jack would miss the match as they continue to manage his return from injury.
Rangers started with Jack Butland in goal and a back four of James Tavernier, Connor Goldson, John Souttar and Ridvan.
Tom Lawrence joined John Lundstram and Todd Cantwell in midfield, while Rabbi Matondo and Ross McCausland provided the width with striker Cyriel Dessers leading the line.
For the visitors, it was Neil Warnock’s first match in charge after being announced as their manager until the end of the season earlier in the week.
Rangers got the action underway, as Philippe Clement looked for his side to continue their recent form and there was a fantastic atmosphere inside the stadium.
It was a lively start and the home side almost had an early breakthrough after Rabbi Matondo and Tom Lawrence linked-up well, with the former picking out a pass to find the run of Todd Cantwell. In a good position in the box, Cantwell looked for Cyriel Dessers but Aberdeen managed to clear to prevent the ball from reaching the Rangers number nine.
The early pressure from Rangers did pay off shortly after and it was the second goal in the space of three days for Rabbi Matondo with just seven minutes played.
The winger started the move winning the ball back just inside the Aberdeen half before finding Cantwell who fed it out to the right to Ross McCausland. The youngster cut inside and in space drilled a low shot towards goal which Kelle Roos in the Aberdeen goal was unable to hold.
Matondo was in the perfect position having carried on his run into the box and followed-up the rebound firing a composed left-footed finish into the back of the net.
In another good move for Rangers, McCausland was denied by Roos, before James Tavernier was unable to keep a rebound shot on target as the Light Blues pushed to increase their advantage.
There was almost a second for Rabbi Matondo with 38 minutes played as Todd Cantwell released the winger down the left. The Welshman did well to cut inside, beating two Aberdeen defenders but opted to take the shot, which was blocked by a defender in the box.
Matondo had another strike at goal as he got on the end of a flick on from Cyriel Dessers but his powerful effort was saved by Roos.
In another attack, John Souttar picked out Ridvan’s run into the box and he cut the ball back from the byline in search of Cyriel Dessers but his low shot bounced just wide of the goalkeeper’s left-hand post.
Despite the Rangers dominance, Aberdeen managed to find an equaliser on the stroke of half-time. A long ball over the top was sent forward by Connor Barron, with Bojan Miovski nipping in behind the Rangers defence to get his left-foot on the ball and tap it beyond Jack Butland.
Early in the second-half, Nicky Devlin flicked a header towards goal after a Connor Barron corner as the visitors looked to cause Rangers problems after the break.
A chance for Rangers saw Matondo denied by Roos before Dessers follow-up was also blocked by the Aberdeen goalkeeper but the linesman raised his flag for offside.
With just 10 minutes of the second-half played, Clement turned to his bench for the first time this evening as January signings Fabio Silva and Oscar Cortes were introduced in place of Cyriel Dessers and goalscorer Rabbi Matondo.
Silva headed wide from a Ridvan cross, before Roos pulled off a superb block with his foot to deny Tom Lawrence.
Rangers were back ahead with just under 20 minutes remaining at Ibrox. It was again Lawrence who had a long-range strike blocked by Roos, but Todd Cantwell followed up the rebound to mark his 50th competitive appearance for the club with a goal.
Clement turned to his bench again in the 74th minute with Tom Lawrence replaced by Dujon Sterling for the final period of the match before Mohamed Diomande was handed his Rangers debut with just over five minutes remaining at Ibrox as he came on in place of Todd Cantwell.
Miovski flicked a Duk cross towards goal as Aberdeen tried to find a late equaliser, but it was held comfortably by Butland.
Dujon Sterling was shown a straight red card with a few minutes of the 90 remaining as he challenged Jack MacKenzie in the middle of the pitch. Don Robertson was called to the VAR monitor to review the footage, and stood by his decision as Sterling made his way up the tunnel.
Fabio Silva dragged a low shot just wide of the target as Rangers looked to make the end of the match more comfortable, with 8 minutes added on in injury time but Rangers saw it out to pick up a big three points in the league.
RANGERS: Butland, Tavernier, Goldson, Souttar, Ridvan, Lundstram, Lawrence (Sterling, 74), Cantwell (Diomande, 85), Matondo (Cortes, 56), McCausland, Dessers (Silva, 56).
Subs: McCrorie, Wright, Barisic, King, Raskin.
Aberdeen: Roos, Devlin, MacKenzie, Shinnie, Jensen, Gartenmann, McGrath (Duk, 76), Barron, Miovski, Clarkson (Philipps, 76), Hayes (Polvara, 68).
Subs: Doohan, Sokler, Morris, Duncan, MacDonald, Milne.