While the 5-0 scoreline in their favour flattered the home team, this victory will improve their fragile confidence after the departure of former manager Paul Le Guen.
Though outplayed by United in the first half, Rangers still went in two ahead at half time thanks to a marvellous 40-yard strike by Charlie Adam and Chris Burke's close-range header.
With the gale at their backs in the second half, Kris Boyd helped himself to a double before recently restored captain Barry Ferguson finished off the scoring two minutes from time.
Early in the first half keeper Allan McGregor was caught out of position but Karl Svensson cleared Craig Conway's shot off the line.
The Rangers strikeforce of Boyd and Dado Prso were repeatedly being caught offside but against the run of play the home team took the lead.
Derek Stillie was well out of his goal when his attempted clearance broke off Boyd to Adam who struck a 40-yard left-foot shot sweetly into the vacant goal.
United Striker Jon Daly pulled his shot wide before Rangers added to their lead. From Adam's cross Boyd mis-cued his header but Burke followed up and was able to head home.
Despite missing several good chances in the first half, Boyd netted Rangers' third when he curled home Nacho Novo's early cross. The Spanish player injected some much needed pace in the attack after coming on for Prso.
Boyd clinically headed home Ian Murray's cross before Ferguson made it five when he ran on to Boyd's header and rounded the keeper before sliding his shot home.