Despite an improved second-half from the young Gers, a double from Lewis Moore in the first-half was enough for the Edinburgh side.
The match was an excellent challenge for the B Team, with seven under-18 Academy players involved against a number of experienced Hearts first team players, including Scotland international Christophe Berra and goalkeeper Zdenek Zlamal.
Hearts started strongly and put the Gers under pressure inside the first five minutes. Harry Cochrane set up Connor Smith but his shot from the edge of the box was just over the bar.
Rangers were forced into an early change when captain Ben Williamson went down following a strong challenge at the half-way line. The midfielder was taken off on a stretcher, with Cole McKinnon coming into the Gers midfield.
The visitors continued their early pressure as Lewis Moore’s cross was diverted towards goal by Euan Henderson but Nicky Hogarth stood tall to block the effort.
Hearts did get the breakthrough on the 24th minute as Elliot Frear’s corner into the box was eventually fired home by Lewis Moore from close range.
The Edinburgh side had a second just five minutes later as Moore latched on the end of a through ball from Harry Cochrane. Moore took a touch beyond Nicky Hogarth before firing into the back of the net.
Rangers searched for a response before half-time as Ross McCausland picked out Dapo Mebude on the edge of the box but the striker dragged his shot just wide of the target.
Early in the second-half, Kevin Thomson and Brian Gilmour made a few changes to the side with Matthew Henderson and Zac Butterworth coming on in place of Arron Lyall and Robbie Fraser.
Ross McCausland was fouled on the edge of the box as Rangers were awarded a free-kick in a dangerous position. Alex Lowry stepped up to take the set-piece but his right-footed effort was held by Zdenek Zlamal.
Shortly after, Matthew Henderson played a dangerous cross into the box which Dapo Mebude flicked towards goal but it was just wide of the target.
In the final stages of the match, Lewis Moore chipped an effort just over the bar as the Hearts midfielder searched for his third goal of the game.
RANGERS: N. Hogarth, Devine, Fraser (Henderson, 55), Miller (Balde, 71), O’Connor, McClelland, Lyall (Butterworth, 55), Williamson (McKinnon, 8), McCausland (Lindsay, 71), Lowry, Mebude. Subs not used: J. Hogarth.