A first league goal for Colette Cavanagh and a Kayla McCoy strike gave Gers the early advantage, before Cavanagh netted her second of the afternoon with Rachel McLauchlan and Lisa Martinez also on the scoresheet.
It was a dominant display from the Light Blues as they maintained their 100 per cent start to the league campaign.
Malky Thomson named five changes to his team from the midweek victory over Spartans with Maddie Nolf, Kirsty Maclean, Colette Cavanagh, Jodi McLeary and Kirsty Howat all coming into the starting XI.
Rangers lined-up at Broadwood with Victoria Esson in goal and a back four of Nicola Docherty, Lisa Martinez, Hannah Davison and Maddie Nolf.
Jodi McLeary came in for her first league start of the season and was joined in midfield by Kirsty MacLean, Sam Kerr and Colette Cavanagh.
Thomson opted for two strikers this afternoon with Kirsty Howat and Kayla McCoy leading the line for Gers.
It was the first meeting of the campaign with Dundee United, who were promoted as SWPL 2 champions last season. From the first whistle, Rangers showed their intent and it paid off as they had the opening goal with just over two minutes on the clock.
A Gers corner saw the ball fed back out to Nicola Docherty who picked out the run of Colette Cavanagh who took a touch inside the box before directing a left-footed shot towards goal. Despite the efforts of Dundee United defender Lisa Ryan on the line, the ball landed in the back of the net to give Cavanagh her first goal in Light Blue.
It was a fantastic start from Gers, with Kayla McCoy doubling the advantage just a few minutes later. A lovely ball forward from Maddie Nolf picked out the run of McCoy who showed her composure to touch the ball beyond goalkeeper Fiona McNicoll and into the back of the net.
Rangers were hungry for goals at Broadwood and continued to threaten in the early stages with both Sam Kerr and Kirsty Howat seeing efforts saved by McNicoll.
McCoy almost had her second of the afternoon as she linked up well with Colette Cavanagh but her strike at goal was blocked by the Dundee United goalkeeper.
Kirsty Howat came close with a long-range effort as the game passed the half-hour mark with McNicoll at full stretch she was unable to get a hand to the shot but it bounced just wide of the post.
The pressure was relentless from Rangers and they had their third goal of the afternoon in the 33rd minute. A corner was swung into the box by Maddie Nolf and in a busy area Kayla McCoy managed to get a touch to head it into the path of Colette Cavanagh. Her powerful shot managed to make its way through the bodies in the box and into the back of the net for her second goal of the afternoon.
Malky Thomson made one change to his side at the break as Rachel McLauchlan was introduced in place of Nicola Docherty, with Sam Kerr taking the captain's armband for the second-half.
With just over a minute on the pitch, McLauchlan was on the scoresheet as Rangers increased their lead to four goals at Broadwood. It was fantastic play from Kirsty Maclean on the left as she drove towards goal creating space to deliver a ball across the face of goal which Rachel McLauchlan was on hand to tap home.
Hannah Davison came close to adding to the tally shortly after as she headed a Maddie Nolf corner towards goal but it was cleared off the line by a United defender.
In the 57th minute, it was 5-0 as Rangers once again caused problems from a set-piece. The delivery from Maddie Nolf fell for defender Lisa Martinez in the box and she struck a powerful shot high into the back of the net for her fourth goal of the season.
With half an hour of the match remaining, Thomson made two changes to his side as Sam Kerr and Colette Cavanagh were replaced by Dina Orschmann and Jenny Danielsson, with Rachel McLauchlan taking on the armband.
Kirsty Howat came close to getting on the scoresheet as she turned a Rachel McLauchlan cross towards goal but couldn’t keep the effort down as it drifted over the bar.
Two more substitutes were introduced for Rangers for the closing period of the game as Brogan Hay and Emma Watson came on in place of Kayla McCoy and Kirsty Maclean.
Dina Orschmann had a good opportunity to add to the scoring in the final stages of the match with a shot from inside the box but it was just wide of the target.
Attention for Malky Thomson’s side now turns to next weekend’s Sky Sports Cup semi-final away to Spartans.
RANGERS: Esson, Docherty (McLauchlan, 46), Martinez, Davison, Nolf, Maclean (Watson, 75), Kerr (Orschmann, 60), Cavanagh (Danielsson, 60), McLeary, Howat, McCoy (Hay, 75).
Subs not used: Fife, Middag, Cornet.
Dundee United: McNicoll, Donald, Ryan, McLaren, McGinley, Smith (Guthrie, 46), Todd (Delworth, 20), Foote (Malcolm, 82), Bonner (Clemison, 62), Cowper, Harkin (Robb, 62).
Subs not used: McMillan, Fraser, Arthur, Mitchell.