Chelsea Cornet’s volley was the difference at the break in a tight first-half at Broadwood before Lizzie Arnot and Libby Bance found the back of the net in the final 15 minutes of the match in North Lanarkshire.
Fresh off the back of Saturday’s Scottish Cup semi-final victory over Celtic, Jo Potter’s side returned to league action as the intense split schedule continued.
From the weekend, the Gers boss named four changes to her side with Lizzie Arnot, Jodi McLeary, Kirsty Howat and Rio Hardy coming into the team in place of Mia McAulay, Rachel Rowe, Janes Ross and Sarah Ewens.
Rangers started with Victoria Esson in goal for the third match running, while Rachel McLauchlan, Kathryn Hill and captain Nicola Docherty were all in the side once again.
Brogan Hay retained her place alongside Liv McLoughlin and Chelsea Cornet, with Arnot and McLeary joining the line-up. Howat and Hardy both came in from the start for this one after appearing from the bench to make an impact in the cup win.
An early chance for Rangers saw a quick throw in from Chelsea Cornet played into the path of Rachel McLauchlan on the right flank and she returned the ball to Cornet but the midfielder’s powerful strike was blocked by a Hearts defender in the box.
At the other end, the visitors threatened through Kate Mooney as she released a low drilled effort towards goal from the edge of the area, but it was wide of the right-hand post.
There was a break in play with 10 minutes on the clock and a blow for Hearts as their captain Georgia Hunter was forced off through injury, with Jessica Husband coming off the bench.
From a corner, Rangers managed to find the breakthrough and for the second time in four days it was Chelsea Cornet who produced the opening goal. Lizzie Arnot swung a dangerous corner into the box, with Kathryn Hill getting first contact with a header before Cornet was alert to send a superb volley beyond Parker-Smith.
It was a dominant start from Rangers at Broadwood, and another fine move saw Brogan Hay find Lizzie Arnot on the opposite flank with a lovely crossfield pass. Arnot took a touch before cutting inside onto her right-foot and curling a shot toward goal, but it was just wide of the target from the Scotland international.
Shortly after Arnot again threatened from distance, and this time forced a good save from Parker-Smith as her strike looked to be heading for the back of the net.
With a narrow lead at the break, Potter turned to her bench at the break with Rachel Rowe introduced in place of Brogan Hay.
Kirsty Howat had a shot blocked early in the second-half as Rangers looked to make things a bit more comfortable by increasing their advantage at Broadwood.
The Light Blues were knocking at the door for a second after Chelsea Cornet did well to win the ball back in the middle of the pitch to release Rio Hardy down the right. With space, the forward cut the ball across goal with it almost breaking for Lizzie Arnot at the back post, but the visitors were able to deal with the danger.
Potter made a change up front for the final 20 minutes of the match as Sarah Ewens came on to replace Kirsty Howat.
The all-important second goal did come for Rangers as they increased their advantage with a fine strike from Lizzie Arnot.
It was Rachel Rowe who gathered the ball in a central area before finding the run of Arnot just inside the penalty box and she tucked a fine strike into the bottom corner.
Tessel Middag was next to be introduced from the bench as Rangers looked to see out the final 10 minutes of this match, with Jodi McLeary replaced.
Chelsea Cornet headed wide a Middag cross late in the match as the Light Blues continued to dominate at Broadwood.
Rangers made it three in the final stages of the match, as Libby Bance, who had only just entered the field, found the back of the net. The on-loan Brighton midfielder gathered the ball on the edge of the box and guided a left-footed finish beyond Parker-Smith to secure the points for Rangers.
RANGERS: Esson, Docherty, McLauchlan, Hill, Hay (Rowe, 46), Howat (Ewens, 70), Hardy (Ross, 87), Arnot, Cornet, McLoughlin (Bance, 87) McLeary (Middag, 79)
SUBS: Fife, Austin, Martinez
HEARTS: Parker-Smith, Brownlie, Hunter (J. Husband, 12), Grant, Forsyth (Michie, 61), Lockwood (Adamolekun, 61), Waldie (E. Husband, 61), Handley, Mooney (Chomczuk, 81), Girasoli, McGovern.
Subs: Johnstone, Penman, Rennie.