In an opening half hour where few chances separated the sides Jane Ross was on hand to fire home the only goal of the game as her strike was the difference to send the Gers on their way to another three points.
Head coach Jo Potter named two changes to the team that ran out 9-0 winners over Dundee United in the Scottish Cup at the weekend, with Lizzie Arnot and Chelsea Cornet coming in to replace Eilidh Austin and Jodi McLeary.
Both sides started the match with comfortable early possession. As the Light Blues looked for another early goal as they did at the weekend but there were no clear cut openings in the early stages in Cumbernauld.
The first real opportunity of the evening fell the way of the hosts. Rachel Rowe and Lizzie Arnot combined to work the ball from left to right, the initial pass from Brogan Hay was deflected back into the path of the Rangers number 15, but her shot flew over the top of the bar and behind.
Hearts had their first chance of the night just after the quarter-hour mark. Winning the ball high the Jambos worked the ball from right to left a chance presented itself for Olufoasade Adamolekun but her shot was dragged wide of post.
Rachel Rowe had a tremendous effort range turned round the post well by Charlotte Parker-Smith. The Wales international tried her luck from 25 yards out which was heading for the top corner, but the goalkeeper did well to make the stop.
After a closely fought opening half Rangers took the lead. Rowe did superbly well to ride multiple challenges as she carried the ball into the Hearts half. Opting against using Hay down the right flank she chopped back onto her left foot before sliding the ball through to Jane Ross. The striker composed herself inside the area and fired the ball into the corner on her left side to fire the Gers ahead.
The Gers looked to build on their 1-0 lead at the start of the second half. Rowe was finding space in dangerous areas and looked the most likely to manufacture further chances as the hosts looked to go further in front, but the away side were more than holding their own.
Georgia Timms, who looked the most likely for the visitors did well to create an opportunity of her own. Running the flank she had Nicola Docherty close for company and opted to shoot from a tight angle, but her shot sailed over the top of the bar.
Lizzie Arnot almost created a first chance of the night for Rio Hardy. The winger made herself a yard on the flank before sending in a cross which looked for the striker, but the delivery was just too high as she lacked the desired power to trouble Parker-Smith with her headed effort.
Hardy went agonisingly close to doubling the lead but for a point blank save by Parker-Smith. A fortune break of the ball allowed Rowe to advance and combine with Arnot. The winger clipped the ball into the area which was met by the head of the forward who kept the effort on target but was kept out by the shot stopper.
Chances at both ends remained few and far between as the Light Blues saw the match out to claim a second win in three days as attention now turns to another SWPL fixture against Partick Thistle.
RANGERS: Fife, Hill, Middag, Docherty, Hay (McAulay 68), Cornet, McLoughlin, Arnot (McLeary 90+2), Rowe, Ross, Hardy (Ewens 68)
SUBS: Inman, Austin, Martinez
HEARTS: Parker-Smith, Brownlie, Hunter, Grant, Timms (McGinley 77), Waldie, Adamolekun, Handley (Penman 63), Mooney, Girasoli, Michie (Rennie 54)
SUBS: Johnstone, Lockwood, Chomczuk, Brien, Low