Laura Berry got the scoring underway for Leanne Crichton’s side midway through the first half, and her goal was soon supplemented by Bailley Collins who continued her early purple patch in front of goal this season.
A third was added by the irrepressible Berry shortly into the second period as Rangers made it three wins on the spin to open their league campaign.
From the team which defeated Spartans, who also play their home games in the north of the capital, last weekend, in came captain Nicola Docherty, Gry Boe Thrysoe and Mijke Roelfsema.
It was the home side who fashioned the first attempt at goal when Carly Johns drove through the heart of the pitch and struck straight down the throat of Shu Obha, making her second successive start between the posts.
Now coached by former Gers assistant, Andy Thomson, the capital club pieced together a neat move on 13 minutes which ended at the feet of full-back Jessica Husband who curled over from distance.
Rangers were beginning to look bright down the flanks, and just ten minutes later it was Bailley Collins who broke into space down the right. She played a lovely give-and-go with Calliste Brookshire on the corner of the penalty box but could only steer a curling effort off target on her unfavoured left side.
The visitors again threatened minutes later when Brookshire was released down the left and her cross was only headed back into a dangerous area by Katie Wilkinson at the far post and eventually cleared to safety.
And just 60 seconds later, the Gers capitalised on their momentum.
It was a swift transition which unpicked the hosts’ defence, with Wilkinson lifting her head to feed Berry through on goal and the Scotland youth international composed herself to slide a delicious finish into the bottom corner.
Rangers were rampant by this point, and they doubled their advantage five minutes later with a gorgeous pass out of defence by Mijke Roelfsema.
Collins was the beneficiary with a darting run from full-back, piercing straight through the heart of the Hearts defence before dispatching a wonderful volley into the far corner.
Crichton’s side picked up exactly where they left off to open the second half, with a third of the afternoon arriving just three minutes after the interval.
A cross from the left trickled all the way through to the far post where Berry was lurking as all good forwards do to lash a thunderous effort beyond the Hearts goalkeeper at full stretch.
Obha in the Rangers goal was having very little to contend with, but she showed why she has proved such a valuable summer addition when she sprung down low to thwart Mariana Speckmaier after the Hearts forward swivelled smartly inside the penalty box and fired low towards goal.
The away side went in search of a fourth when Brookshire burst down the left and Hearts could only clear as far as Jodi McLeary, but the midfielder’s first-time effort sailed off target.
The crossbar was later rattled by a deflected Brookshire strike, and as the heavens opened in Edinburgh and the pitch became submerged in water, the game played out to a conclusion with the Gers securing a priceless three points.
RANGERS: Obha, Collins (Smith, 75), Austin, Roelfsema, Docherty, Cruft (Black, 75), Thrysoe, McLeary (Blake, 57), Berry (Hay, 81), Brookshire (Hendle, 81), Wilkinson
Subs not used: Fife, Boyce, Connolly-Jackson
HEARTS: Johnstone, J. Husband, E. Husband, Girasoli, Forsyth, Fulton, Speckmaier, Johns, Wade, Dolan, Jardine
Subs: Anderson, Rennie, Smith, Halliday, Crawford, Fraser, Robertson, Campbell, Horberry