© Lynne Cameron / PA Photos
The home side were quick out of the blocks, taking the lead after just 13 seconds through Johnny Russell, who struck the ball past the Rangers keeper from inside the penalty box.
United continued to dominate the first half, and doubled their lead in the 36th minute with Jon Daly heading the ball in from close range.
Rangers took a more physical approach after the break and were able to contain their opponents more effectively, but also drew the attention of the referee, racking up five yellow cards.
A scrappy end to the match saw Kal Naismith shown a straight red for a dangerous challenge on Willo Smith, before Ian Black was dismissed for securing his second yellow of the match just two minutes later.