The home side, inspired by the rampant Gary Mackay-Steven, had gone in front through Ryan Gauld; Kenny McLean levelled from the penalty spot before Ciftci’s coup de grace sealed their first win since Christmas.
On a decent pitch in front of a healthy crowd, there was plenty to encourage the faithful in a bright opening.
Steven Thompson worked home keeper Radoslaw Cierzniak while United skipper Stuart Armstrong’s deflected strike was well held by Marian Kello at his near post.
The open pattern of play continued as Mackay-Steven sliced down the left but Armstrong could not provide the requisite finish from 18 yards.
When Ciftci skipped clear of debutant Eric Djemba-Djemba, he laid the ball across goal for Gauld (21) to slide in and finish from six yards.
Saints were level five minutes later thanks to McLean’s penalty after the midfielder himself had been clipped by Mark Wilson.
The action soon swung back to the other end, MacKay-Steven forcing a decent stop from Kello, who also produced another fine reaction save to repel Ciftci’s close-range header.
Ciftci made amends for that miss five minutes after the break when – after a spell of sustained pressure – he rose to head home the irrepressible Mackay-Steven’s chipped cross.
Kello tipped over Gauld’s stinger as the home side continued to attack with incision and purpose down the left-hand side.
Saints did rally briefly in the final quarter – Thompson drawing a flying stop from Cierzniak with a bullet header – but it was the 2010 winners who were to advance to the last eight, when they will travel to either Stranraer or Inverness.