Lizzie Arnot opened the scoring in the first-half for Gers with Nicola Docherty and Brianna Westrup adding to that in the second-half.
Malky Thomson named two changes from the opening day victory over Hamilton with Emma Brownlie coming in for her first start of the season after recovering from injury with Zoe Ness also making the starting XI.
Rangers started brightly and had a chance in the early stages of the match as Emma Brownlie delivered a ball in from the right which was headed just over the bar by Lizzie Arnot, before Jane Ross came close as she curled a shot over the bar.
In the 18th minute, Demi Vance whipped a ball in from the left to pick out the run of Jane Ross but she couldn’t get a strong enough connection with the ball as she tapped it goalwards but it was gathered by goalkeeper Charlotte Parker-Smith.
Rangers got the breakthrough on the 25th minute as Lizzie Arnot opened the scoring at Oriam. Zoe Ness did well to put pressure on a Hearts defender to win the ball back before feeding in Jane Ross. The striker picked out Arnot on the edge of the box and she curled a lovely right-footed shot into the back of the net.
Ross glanced a header just wide of the target before the break as Rangers looked to increase their advantage ahead of the interval.
Into the second-half, the Light Blues continued to dominate as Chelsea Cornet dragged a shot just inches wide of the post.
In the 57th minute, Brogan Hay picked out Jane Ross in the box and she turned well to get a shot away but it was just over the bar.
Just after the hour mark, Malky Thomson made three substitutions with Kirsten Reilly, Brogan Hay and Emma Brownlie being replaced by Tessel Middag, Rachel McLauchlan and Nicola Docherty.
Docherty was involved instantly as she doubled Gers’ avantage after only three minutes on the pitch. Tessel Middag picked out Docherty who drilled a right-footed shot into the back of the net.
It was 3-0 on the 85th minute as Lizzie Arnot delivered a corner into the box which fell for captain Brianna Westrup who drilled a powerful shot into the back of the net from inside the area.
Rangers now turn their attention to Spartans at home in the SWPL on Wednesday evening.
RANGERS: Fife, Vance, Brownlie (McLauchlan 63), Hay (Docherty, 63), Reilly (Middag, 63), Ness (Watson, 79), Ross (McLeary, 86), Arnot, Cornet, Westrup, Swaby, Cunningham.
Subs: Cunningham, Arnth.
HEARTS: Parker-Smith, Delworth, McKay, Hunter, Browning, Kaney, Tweedie, Smith, Birse, Cowan, Anderson.
Subs: Tebbitt, Forsyth, Aitchison, Handley, Davies, Thomson, McAneny.
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