Nacho Novo burst clear of the United defence to open the scoring after seven minutes, taking the ball around the on-rushing Nick Colgan before slotting the ball into the empty net.
Dado Prso doubled the lead in the 17th minute with a looping header when he met Marvin Andrews' free-kick with a diagonal header from 15 yards which went in off the far post.
Novo saw his 38th minute penalty saved by Colgan after a tangle between Paul Ritchie and Prso but United then surprisingly pulled a goal back when substitute Jason Scotland drilled the ball home from 12 yards.
Thomas Buffel restored Rangers' two-goal cushion in the 67th minute when he forced in a fierce low cross from Novo and a minute later former captain Barry Ferguson was brought on as a substitute.
Almost immediately Fernando Ricksen curled in a 20-yard free-kick and Steve Thompson made it 5-1 with ten minutes left when he turned in a Maurice Ross cross.
There was still time for Novo to fire past Colgan and Thompson to make it seven after Colgan spilled a shot from Ferguson.