The victory marked a fourth win in succession for Jo Potter’s side, who have also netted a remarkable 27 goals in that timeframe.
And they certainly didn’t have it all their own way after the Tangerines stunned the home crowd when Morgan Steedman opened the scoring with an opportunistic lob.
However, a brace from Jane Ross prior to the interval, as well as goals from Camille Lafaix, Mia McAulay, Katie Wilkinson and a Kirsty Howat spot-kick turned the game on its head and ensured the points remained with the Light Blues.
The Gers trail league leaders Glasgow City by a solitary point heading into the final international hiatus of the year, with a trip to face Westdyke in the Scottish Cup next up for Potter’s side.
Indeed, Rangers began the brighter of the two sides this afternoon, going close through McAulay when the 18-year-old lashed just wide of the target after pouncing on a loose ball inside the penalty area.
Howat was then next to test her luck when she received a pass from the lively Lafaix, although she could only steer her powerful finish off target from an admittedly tight angle.
The Gers were soon pegged back with fewer than 25 minutes on the clock after Steedman broke into the Gers half and lifted an audacious finish over Jenna Fife who slipped outside of her penalty area at an inopportune moment.
However, the Light Blues responded positively when Lafaix sprung the offside trap and, after squaring across the face of goal for Howat, Ross was on hand to slam the ball beyond Beth Mowatt in the Dundee United goal.
The turnaround was soon complete for the hosts when Ross, already brimming with confidence, arrowed an unstoppable effort from 25 yards into the top corner in one of the strikes of the campaign for the Gers.
The Gers seemed personally affronted by the concession of their opening goal and they stretched their lead in first-half stoppage time when a seemingly innocuous cross from Megan Bell was spilled by Mowatt and Lafaix hared towards goal to bundle the ball over the line.
Potter turned to her bench at the interval as Kathy Hull replaced Tessel Middag, with Eilidh Austin going immediately close to a fourth of the afternoon for Rangers when her side-footed effort was thwarted by Mowatt.
Indeed, the visitors were indebted to their goalkeeper for keeping the scoreline down in the second period, while the woodwork soon denied McAulay and Howat.
The former, however, wasn’t to be denied just beyond the hour-mark when a slick move from the Gers brought the ball into the teenager’s path from close range and she made no mistake in stroking her finish into the bottom corner.
With the Light Blues in an unassailable position, both Katie Wilkinson and Kirsty Maclean were introduced as the hosts searched for a fifth before the conclusion of the contest.
And it arrived from a dead ball situation after a delicious inswinging delivery from Lizzie Arnot was volleyed home from three yards out by Wilkinson who continues her remarkable goalscoring campaign.
There was still time, meanwhile, for Rangers to add their sixth of the contest when Howat, who had been denied repeatedly by Mowatt, was felled inside the penalty area and she made no mistake from 12 yards in dispatching the resulting spot-kick beyond the United goalkeeper.
RANGERS: Fife, Rafferty, Middag (Hill, 45), Howat, Bell (Maclean, 56), Ross (Hardy, 70), McAulay, Arnot, Austin, Cornet (McLeary, 77), Lafaix (Wilkinson, 56)
Subs not used: Esson, Docherty, McLoughlin
DUNDEE UNITED: Mowatt, Frew, Cusack, Robertson (McFadyen, 45), Sidey, Christie (Martindale, 70), Cowie, M.Steedman (Logan, 65), Burns, Knight (Moodie, 40), Brien
Subs not used: Rennie, Osborne, Taylor, Hutchison, L. Steedman