The young Gers found themselves with a mountain to climb when the Edinburgh side struck twice early in the game.
Their strength in the contest grew slowly, yet it was the visitors who stretched their advantage further just beyond the hour-mark.
However, a stunning comeback saw Rangers net three times in the final 22 minutes through Conor Owen, Cameron Fernie and James Reid to salvage a point.
From the team which defeated Dundee United on the opening matchday seven days ago, in came Josh Gentles and Ashton Patton.
But the opening minutes mirrored last week at Foundation Park as the Gers fell behind early.
This time, the ball broke to Euan Glasgow 30 yards from goal and, with time and space opening up, he took on the invitation to shoot low from the edge of the penalty area and into the bottom corner.
The away side quickly doubled their advantage when Jaedon Doncker did well down the right-hand side before pulling the ball back to Jayden Mathie, who slammed beyond Sam Reid.
Callum Burnside had the hosts’ first chance in anger, but his curling effort was always on the optimistic side as it sailed wide.
The relative experience of Josh Gentles and Burnside, who spent time together on loan at Alloa Athletic last term, looked effective in tandem as the pair combined before the latter shot straight at the goalkeeper.
Ashton Patton was unfortunate not to pull a goal back on the half-hour mark when he collected a Burnside crossfield pass and forced the goalkeeper into a smart save.
A glancing header from Ben Hutton went wide moments later, while Gentles passed up an opportunity five minutes before the interval after spurning over the crossbar from close-range.
The Gers were firmly on top, and Luca Rankin was next to threaten when he glided into a dangerous shooting area and was thwarted by another good save from the Hearts goalkeeper.
For all of Rangers’ pressure, however, it was the away side who stretched their advantage just beyond the hour-mark.
A Hearts foray forward saw the ball moved wide to the dangerous Doncker who worked a half yard of space and curled out of the reach of Sam Reid into the far corner.
The hosts eventually got the goal that their play merited just five minutes later, reducing the deficit when Owen netted for the second successive week after meeting Rankin’s free-kick delivery at the far post to nod low into the bottom corner.
Three minutes later, the comeback suddenly appeared possible.
After play moved to the left-hand side, Coben Fergusson saw his effort cannon off a maroon jersey, but the ball broke kindly to Fernie at the edge of the penalty area and the midfielder dispatched with aplomb beyond the goalkeeper.
Burnside then threatened with an acrobatic effort that would have been worthy of crowning a comeback in any fixture.
A direct move from Rangers involving Gentles, Burnside and Patton almost led to the latter firing home from the edge of the penalty area.
And from the resulting corner, the leveller arrived with five minutes to go.
The young Gers showed their set-piece prowess once again as a Burnside delivery was met by James Reid, who powered a thunderous header beyond the goalkeeper.
A matter of inches separated Burnside from connecting with Gentles inside the six-yard area, which was all she wrote following a breathless second-half comeback.
RANGERS: S. Reid, Patton, J. Reid, Owen, Wark (Fernie, 45), Hutton, Young, Rankin, Fergusson, Burnside, Gentles
Subs not used: Millarvie, Ramage, Ngwenya, Mensing, Hall, Owoyomi
HEARTS: Duncan, Glasgow, Flockhart, McGauley, S. Wilson (A. Clark, 45), Sanders (Willox, 73), North (Dow, 45), Donkor, Kellock (C. Clark, 70; Kaharevic, 83), Mathie, A. Wilson
Subs not used: Jamieson
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