Ciftci got in behind Lee Mair and slipped the ball past the advancing Marian Kello to break the deadlock at Tannadice after 27 minutes.
And the United striker stuck again with a well taken penalty seven minutes later after he had been brought down by Sean Kelly.
Gauld put the game beyond the visitors when he cut in from the flank and dispatched a wonderful drive from 25 yards past Kello.
The Buddies arrived on Tayside undefeated in the last three matches but were on the back-foot from the start, surviving an early scare when Brian Graham just failed to connect with Gary Mackay-Steven's low centre.
Gauld twice came close to scoring towards the end of the opening period when he drilled just wide of the target and then forced Kello into action in injury-time.
And United could have added a fourth when Graham, Gauld and Ciftci were denied inside the six-yard box.
But Erskine did add the fourth when the United substitute crashed home from distance 10 minutes from the end.