Indeed, the Gers appeared to be heading towards victory when Katie Wilkinson struck twice in as many second half minutes to complete a dramatic turnaround following Olufolasade Adamolekun's opener in the first half.
However, the visitors rescued a point when captain Eilidh Shore struck with just two minutes remaining in the contest as Rangers were forced to settle for a point in Leanne Crichton's first Ibrox match in charge.
The Gers boss named the solitary change from last weekend’s rout at Links Park as Alice Griffiths replaced Kirsty Howat.
It was Hearts, however, who fashioned the first opportunity of the contest when a searching delivery from the left-hand side was met by Monica Forsyth and headed over the top of Jenna Fife’s goal.
The home side were slow out of the traps and survived another scare when Lauren Wade centred for Georgia Timms in acres of space, although fortunately for Rangers she contrived to steer her first-time volley wide of the target.
Katie Wilkinson then endeavoured to inject some life into the hosts when she profited from a regain in the final third, but her volley from distance was always speculative and sailed high.
But the Gers suffered a setback just shy of the half-hour mark when Hearts sprung forward on the counter-attack, combining neatly through Carly Johns and Olufolasade Adamolekun before the latter curled an unstoppable effort beyond Fife to break the deadlock.
The visitors had their tails up as a result and a cross-cum-shot from Forsyth on the right-hand side clipped the top of the crossbar much to the relief of the Light Blues.
The woodwork, however, was rattled down the opposite end just moments later as Wilkinson was bemoaning her misfortunate when she steadied herself from a Mia McAulay pull-back and pulled the trigger.
Rangers required a response in the second half and they very nearly got exactly that when a wicked delivery across the face of goal from Brogan Hay forced Rachael Johnstone in the Hearts goal to be at full stretch to divert the danger to safety.
Those in blue were then unanimous in their appeals to referee Mark Daly when Wilkinson sprung the offside trap and appeared to be brought down as she rounded Johnstone, but he looked in the opposite direction despite replays showing contact.
Camille Lafaix then nodded straight down the throat of the Hearts goalkeeper from a corner before there were faint cries for a spot-kick once again moments later when the American midfielder went to ground on the left-hand side of the danger area.
The hosts were certainly ratcheting up the intensity as McAulay’s delivery from the left squirmed through the hands of Johnstone and out for a corner before Jodi McLeary dinked a delicious pass into Wilkinson whose chest control was immaculate but her finish equal to by the Hearts goalkeeper.
Crichton turned to her substitutes bench with the introduction of Lizzie Arnot and May Cruft as Rangers sought an avenue back into the contest.
Dividends were paid immediately when Arnot turned architect for the equaliser, drifting around to the back post from a Hay cross to nod across goal for Wilkinson to stab home from point-blank range.
And it got even better for both the substitute and Rangers when she assumed duties from a free-kick on the left-hand side. Her delivery was on the money and wreaked havoc in the Hearts penalty area where Wilkinson, as all good strikers do, lurked with intent to guide the ball beyond Johnstone to complete a swift turnaround.
However, the visitors had the final say in a dramatic second half as Eilidh Shore knocked home three minutes from time to salvage a point for the Edinburgh side.
RANGERS: Fife, McLeary, Austin, Docherty, Connolly-Jackson, McLoughlin (Shin Ji, 80), Griffiths (Cruft, 68), Lafaix (Howat, 57), Hay (Berry, 80), McAulay (Arnot, 68), Wilkinson
Subs not used: Ivarsdottir (GK)
HEARTS: Johnstone, J. Husband, E. Husband, Forsyth, Shore, Timms, Adamolekun (Jardine, 69), Wade, Waldie (Halliday, 69), Andrews, Johns (Slattery, 76)
Subs not used: Vilao Dias, Ypeman, Greenwood, Chomczuk
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