The striker found the target just six minutes into the game to net his third goal in three matches and secure the points for Clement’s men.
From Thursday’s 1-1 draw away to Olympiacos there were two changes to the starting line-up as captain James Tavernier and Leon Balogun returned to the back four in place of Dujon Sterling and Robin Propper.
That meant Butland started once again for Rangers between the sticks, behind James Tavernier, John Souttar, Leon Balogun and Jefte.
In midfield and attack, Clement stuck with the same six players from Thursday night, with Nico Raskin, Connor Barron and Mohamed Diomande taking up position in the middle of the pitch, while Cyriel Dessers led the line supported by Vaclav Cerny and Nedim Bajrami.
Ibrox fell silent prior to kick-off as the club and supporters paid their respects to the service men and women who have made the ultimate sacrifice for their country. Veterans David Edgar and Steven Davidson led the teams out of the tunnel, with serving members of the Army, RAF and Royal Navy taking part in the pre-match act of Remembrance.
Ahead of the game, manager Philippe Clement said he was looking for his side to build on Thursday’s positive performance in Greece and he would’ve been impressed by the start his team made as they found the breakthrough with just five minutes played.
The move started down the left-hand side with Jefte finding Bajrami further forward and the Albanian delivered the ball into the box. It reached James Tavernier who had made a run from right-back and he blasted the ball towards goal with Cyriel Dessers in the perfect position to get the crucial touch to send it beyond Craig Gordon for his tenth goal of the season.
In the period following the goal, the visitors looked to get a quick equaliser, with a series of set-pieces opening up the opportunity for the Edinburgh side but they were unable to test Jack Butland in the Rangers goal.
Jefte was again involved in creating another opening for Rangers as he drove forward, weaving beyond two Hearts players to get into the box and feed in Cyriel Dessers but it didn’t fall for the striker and the danger was cleared by Hearts.
With 30 minutes played, Diomande came agonisingly close to doubling Rangers’ advantage as Vaclav Cerny cut in from the right to pick out the midfielder on the edge of the box. Diomande took a touch to set up a left-footed shot but dragged it just wide of Craig Gordon’s left-hand post.
Minutes later, Cerny forced a save from the Scotland international goalkeeper as Gordon pushed away a strong strike from the Rangers winger.
Clement’s men were really pushing for a second goal, and another good move saw Bajrami find Dessers on in the left-hand side of the box. He tried to cut it back to Connor Barron who had made a run into the box but a Hearts clearance sent it into the path of Bajrami but he curled his shot just over.
Hearts were almost gifted an opening at the other end, as Kenneth Vargas intercepted a short back pass from John Souttar to Butland, but the Rangers number one was alert to come out and block the danger to ensure a lead at the break for Clement’s men.
A matter of seconds after the break, Hearts had their best opportunity of the game so far. Lawrence Shankland took the ball down well to control it and released Kenneth Vargas one on one with Jack Butland. The striker managed to beat the Rangers keeper with his shot but was denied by the post as the shot bounced back off the woodwork.
With 68 minutes played at Ibrox, Rangers were struggling to get control of this second-half, and Clement turned to his bench for the first time. Dujon Sterling came on in midfield to replace Connor Barron, while Neraysho Kasanwijro replaced James Tavernier at right-back.
Having just come on for Hearts, Baningime threatened with a strike from distance which was just wide of the post. Shortly after, Bajrami forced a save from Gordon after getting on the end of a Cerny cutback, but the goalkeeper pushed away the initial shot before gathering the ball at the second attempt.
Another change followed for Rangers as Clement freshened up his attack with the introduction of Danilo in place of Cyriel Dessers.
Kasanwirjo saw a shot deflected wide in the final 10 minutes as Rangers looked to make it a more comfortable ending to this match before Kieran Dowell and Ross McCausland came on for the final period as they replaced Vaclav Cerny and Nedim Bajrami.
Kasanwirjo was denied by the woodwork late in the match, as he got on the end of a Danilo cross to send the ball off the bar as Rangers held on to their lead to take the points.
RANGERS: Butland, Tavernier (Kasanwirjo, 68), Souttar, Balogun, Jefte, Raskin, Barron (Sterling 68), Diomande, Cerny (Dowell, 85), Bajrami (McCausland, 85), Dessers (78)
Subs: Kelly, Propper, Igamane, Hagi.
HEARTS: Gordon, Kent, Oyegoke, Shankland, Devlin (Drammeh, 78), Rowles, Spittal, Forrest (Dhanda, 68), Boateng (Baningime, 68), Penrice, Vargas.
Subs: Clark, Kingsley, Halkett, Grant, Wilson, Forrester.