First-half goals from Steven Naismith and skipper Barry Ferguson were sufficient to earn the points for the home team.
Rangers should have added to their half-time lead but some poor finishing and a great save by United keeper Euan McLean from a penalty by substitute Kris Boyd kept the scoreline down.
The home side took the lead early in the match. There seemed no immediate danger as Chris Burke cut in from the right, but his accurate cross was headed home from six yards by Naismith, who had cleverly moved in front of Sean Dillon.
United kept possession well but there was no end product to their passing game.
Burke's corner was cleared to Brahim Hemdani, but though he kept his shot from 25 yards down, it was narrowly off target.
The difficult conditions were making crisp passing difficult, but Burke's excellent run ended in the winger firing in a 20-yard shot which McLean saved at full-length.
From the resultant corner, Alan Hutton's header clipped the top of the bar on its way over.
Rangers went two up when Burke's cross from the left was headed home by Ferguson.
The far side official at first flagged for offside against Daniel Cousin, but after discussions the referee allowed the goal to stand.
After the break, Carlos Cuellar did well to block a Morgaro Gomis shot from the edge of the box.
Then Ferguson's clever flick put Cousin through on goal, but rather than shooting first time, the striker went around the keeper and was crowded out.
Hutton showed why he is attracting so much transfer speculation with a powerful tackle on Noel Hunt at the edge of the penalty box before surging up field and combining well with Burke.
Kevin Thomson's clever back-heel found Ferguson but his powerful shot was turned behind by the keeper.
From Burke's cross, Boyd was fouled as he rose to make a header at the back post.
The substitute took the penalty himself but his effort was parried by McLean and the keeper then did well to hold Boyd's follow-up shot.