The Light Blues netted five in a relentless opening period, earned through a brace from Katie Wilkinson and goals from Mia McAulay, Kirsty Howat and a Rio Hardy spot-kick.
Although Hearts offered a response in the second half, Rangers were able to hold the Edinburgh side at arm’s length and will now go toe-to-toe with league leaders Hibernian at Ibrox in Sunday’s league finale knowing only a victory will deliver the league crown they covet so dearly.
Jo Potter named the solitary change to her side from the weekend’s Old Firm triumph as McAulay replaced Brogan Hay.
Temperatures soared in the Scottish capital at kick-off as Rangers looked to turn up the heat in the title race.
Across the opposite side of Edinburgh, news filtered through to the stands that Hibs held a comfortable advantage in their clash against Celtic – kicking off half an hour earlier – which made Rangers’ remit clear: win.
However, it was Hearts who threatened immediately with a hopeful pass over the top of the Gers backline which Georgia Timms latched onto and was only thwarted by an expert last-ditch challenge by the backtracking Jodi McLeary.
Down the opposite end and the Light Blues looked at their purposeful best; Rio Hardy drawing a smart stop from the Hearts goalkeeper at her near post where she perhaps had too much time to think.
Bayley Hutchison then went close for the hosts after she was picked out inside the penalty area, although the forward’s effort was wayward despite having sufficient time to compose herself.
The opener, however, arrived following a moment of quality on 16 minutes. McAulay’s pace was causing issues aplenty down the left-hand side and, when she stood up a delightful delivery in search of Wilkinson, this season’s top goalscorer made no mistake in nodding home from close-range.
The Light Blues advantage lasted no more than 60 seconds as Hutchison was freed beyond the Gers backline before rounding Jenna Fife and slotting home.
Those crammed inside the tightly packed Oriam were certainly getting their money’s worth as, on 25 minutes, Rangers restored their advantage.
Indeed, Rio Hardy was the beneficiary from the penalty spot when Kirsty Howat went down inside the penalty area, with the forward slamming home off the inside of the post from 12 yards.
Hearts retained their attacking threat, underlined when Hutchison struck the crossbar on the half-volley and Jessica Husband nodded wide unmarked, but the away side stretched their advantage just beyond the half-hour mark.
And it was the Academy connection as Kirsty Maclean picked out a gorgeous slide rule pass in the direction of McAulay who swept an outstanding left-footed finish into the top corner.
Rangers were rampant, and it was no surprise five minutes before the interval that they put the game out of sight.
It was a familiar source as the excellent McAulay once again jinked down the left-hand side and crossed on the money for Wilkinson who found a half yard of space inside the danger area and powered a header into the top corner.
The half-time whistle couldn’t come quickly enough for the hosts, but they were unable to stem the bleeding as four swiftly became five in first-half stoppage time when Howat swivelled inside the penalty area and curled deliciously into the top corner.
Hearts reduced the arrears just moments into the second period when an errant pass from Fife was pounced upon by Eilidh Shore who lobbed the stranded goalkeeper from distance.
With such a cushion in the contest, Potter turned to Jane Ross on the hour-mark as the forward marked her penultimate professional appearance in the game.
Shore tested her luck once again for the Jambos moments later, but it was no trouble for Fife on this occasion.
She was, however, called into an acrobatic stop when Hutchison held off Tessel Middag and advanced towards goal, curling a dangerous effort which required the Rangers goalkeeper to be at full stretch to claw around for a corner.
A dangerous delivery from Hay was almost turned into her own net by Addison Handley in what was a fleeting moment of danger from the visitors – alongside a disallowed Camille Lafaix effort – in the second half.
The home side netted a third of the evening to restore some optimum when Hutchison glanced a smart header into the bottom corner, but, despite some late nerves, were able to stem the endeavour from the hosts to see out a precious three points.
Full focus now shifts to Sunday’s title showdown as the Gers lock horns with Hibernian in Govan.
HEARTS: Johnstone, Brownlie, Robertson, Forsyth (Handley, 59), Shore, Timms, Waldie, Ypema, Adamolekun, Hutchison, Husband (Wade, 59)
Subs not used: Parker-Smith, Jardine, Andrews, Powell, Bum, Young, Slattery
RANGERS: Fife, Docherty, Rafferty (Hill, 78), Middag, Howat (Ross, 59), Hardy (Lafaix, 45), McAulay (McAulay, 66), Cornet, Maclean, McLeary, Wilkinson (Hay, 45)
Subs not used: Esson, Berry