For Rangers, it was an unchanged team from the Old Firm match a few weeks ago, while deadline day signings Derek Cornelius and Youssef Chermiti were named in the matchday squad for the first time.
Jack Butland started in goal behind a back four of James Tavernier, John Souttar, Nasser Djiga and Jayden Meghoma.
Connor Barron, Mohamed Diomande and Thelo Aasgard were in midfield, while Bojan Miovski was supported in attack by Mikey Moore and Jayden Gassama.
It was the visitors who got the match underway at Ibrox, with Derek McInnes’ side having an unbeaten start to the season in their opening four matches.
Hearts had the first sight of goal from a set piece, with the ball whipped into the box by Alexandros Kyzidris. Devlin met it at the opposite side of the area and returned it back across goal with Craig Halkett heading just high of the target.
Lawrence Shankland saw a sight of goal with five minutes on the clock and tried a low strike on target, but it was comfortably gathered by Butland.
Rangers had a half-chance as the ball broke from an Alexander Schwolow goal kick. Mikey Moore gathered on the left and delivered a cross into the box. Djeidi Gassama struck towards goal but didn’t get the connection he would’ve liked before Jayden Meghoma saw his left-footed attempt blocked.
However, it was the visitors who had the opening goal with 22 minutes on the clock at Ibrox. Captain Lawrence Shankland picked the ball up in midfield and found the run of Claudio Braga who returned it to Shankland and the striker buried a low strike into the bottom corner.
Thelo Aasgaard came closest for Rangers in the first-half as he almost snuck a stunning right footed strike into the top-left hand corner, but it was tipped onto the bar by the Hearts goalkeeper and out for a corner.
Bojan Miovski almost saw the sight of goal as the ball broke for the striker from a Diomande challenge and he tried to touch it beyond the keeper, but Hearts defended, and the goalkeeper gathered before Djeidi Gassama forced a save from Schwolow with a right-footed strike from distance as he cut inside and got a shot away.
Martin made a double change at half-time as he introduced Derek Cornelius for his debut, and Oliver Antman in place of Nasser Djiga and Mikey Moore.
Alexandros Kyziridis had a shot cleared by John Souttar, before Bojan Miovski and Djeidi Gassama looked to launch a Rangers attack at the other end, with the latter cutting a good ball back into the box but the danger was cleared by Hearts.
Another change followed for Rangers with Joe Rothwell introduced in place of Connor Barron with 10 minutes played in the second-half.
James Tavernier flashed a low right-footed strike from outside of the box wide, after Thelo Aasgaard weaved his way into space to pick out the Rangers captain.
Rangers were pushing for the equaliser with Oliver Antman forcing a good save from the goalkeeper, before Aasgaard’s rebound effort was blocked.
Another attack saw the post deny Rangers, this time Tavernier drove Rangers forward before spotting Djeidi Gassama on his left. The winger curled a shot towards goal, but it bounced back off the post.
Youssef Chermiti was handed his Rangers debut with just over 20 minutes remaining as he replaced Jayden Meghoma.
A James Tavernier corner saw Rangers bundle the ball into the back of the net through Derek Cornelius in the 67th minute, but the goal was disallowed by the officials for a foul in the build-up.
Substitute Joe Rothwell, who picked-up an injury earlier in the match, had to be replaced by Nedim Bajrami with 77 minutes played at Ibrox as the visitors also made a triple change.
Hearts were awarded a penalty with just over 10 minutes remaining after Harry Milne went down inside the box. Following a VAR check, the penalty was awarded and Lawrence Shankland stepped-up to the spot.
The initial penalty was saved well by Jack Butland, but the Hearts striker was alert to the rebound and followed-up to double Hearts' advantage.
RANGERS: Butland, Tavernier, Souttar, Djiga (Cornelius, 46), Meghoma (Chermiti, 67), Barron (Rothwell, 57, (Bajrami, 77)), Diomande, Aasgaard, Gassama, Miovski, Moore (Antman, 46).
Subs: Kelly, Aarons, Curtis, Danilo. Hearts: Schwolow, Kingsley (McCart, 75), Halkett, Baningime, Shankland (Spittal, 90), Braga (Kabangu, 75), Devlin, Milne, Findlay, McEntee (Steinwender, 62), Kyziridis (Magnusson, 75).
Subs: Clark, Kabore, Forrest, Kerjota