A Kirsty Howat header was the difference at the break, before Sam Kerr added to that midway through the second-half.
Thomson named four changes to his side from Monday’s draw with Celtic as Victoria Esson, Nicola Docherty, Hannah Davison and Kirsty Maclean came into the starting line-up with Jenna Fife, Tessel Middag and Maddie Nolf on the bench and Lisa Martinez missing out through injury.
Rangers started at Broadwood with Esson in goal and a back four of Nicola Docherty, Hannah Davison, Kathryn Hill and Rachel McLauchlan. Kirsty Maclean joined Sam Kerr and Chelsea Cornet in midfield, while Emma Watson and Brogan Hay supported striker Kirsty Howat.
It was almost the perfect start for Rangers at Broadwood as Howat released a superb strike at goal with six minutes on the clock, but she was denied by the crossbar before the visitors were able to clear the danger.
Rachel McLauchlan did well down the right shortly after as she managed to deliver a good ball into the box in search of Emma Watson but her shot was just wide of Haaland’s right-hand post, before Chelsea Cornet had a powerful strike held by the Hibernian goalkeeper.
Malky Thomson’s side were continuing to search for the breakthrough and in the 27th minute Kirsty Maclean fed the ball through to McLauchlan on the overlap. She directed a cross across the face of goal but Nicola Docherty was unable to find the target with her effort at the back post hitting the side netting.
Hibs were defending well at Broadwood and had their own chance on the break as Nor Mustafa raced towards goal, but captain Kathryn Hill managed to break down the attack with a strong tackle.
Rangers were able to find the breakthrough with 39 minutes on the clock in a well-worked move for the Light Blues. It came down the right flack as Rachel McLauchlan lifted the ball into the path of Chelsea Cornet who had made a run into the box. Cornet sent the ball into a dangerous area with striker Kirsty Howat on hand to head home the opener and her 13th league goal of the season.
In first-half injury time, Joelle Murray denied Rangers a second as she managed to get the ball away on the line after Brogan Hay sent it into a dangerous position in the box.
Thomson made one change to his side at the break as Tessel Middag was introduced in place of Kirsty Maclean.
Early in the half, Hibs came close to getting back level as Lucy Parry struck a powerful shot towards goal with Victoria Esson colliding with the post as she touched the ball onto the woodwork.
At the other end, Brogan Hay flashed a long-range strike just wide of the target after combining well with Kirsty Howat on the edge of the box. Howat was next to have an effort at goal as Tessel Middag played the ball into her path inside the box, but the striker’s low shot curved agonisingly wide of the target.
With 67 minutes on the clock, Rangers doubled the advantage at Broadwood. Brogan Hay played the ball into Kirsty Howat inside the box and she held it up before feeding it out to Chelsea Cornet. Cornet returned the ball into the box and picked out Sam Kerr who turned before blasting a powerful right-footed shot into the back of the net.
A further two changes followed for Malky Thomson’s side as Emma Watson and Kirsty Howat were replaced by Jenny Danielsson and Kayla McCoy.
There were limited chances for both sides in the final 20 minutes of the game, with a lengthy stop in play as Hibs’ Michaela McAlonie received treatment for an injury.
With 5 minutes added at the end of the match, Thomson introduced Megan Bell for the final minutes. Kayla McCoy had a late sight of goal as she got on the end of a long ball forward from Rachel McLauchlan, but Haaland was quick to gather.
There’s an international break next week for the Park’s Motor Group SWPL, with Rangers next in action on Sunday, April 16 as they face Partick Thistle.
RANGERS: Esson, Docherty, Davison, Hill, McLauchlan, Maclean (Middag, 46), Cornet, Kerr (Bell, 88), Watson (Danielsson, 69), Hay (McLeary, 82), Howat (McCoy, 69)
Subs: Fife, Ferguson, Nolf, Berry.
Hibs: Haaland, Leishman, Parry, Hunter, Eddie, McAlonie (Tweedie, 84), Mustafa (Nunn, 64), Notle, Murray, Morrison (Adams, 46), Lawson.
Subs: Kosinska, Kuyken.