The visitors are now the only side in the division still looking for a first win, St Mirren having triumphed at Hearts.
The Tannadice Park showdown got off to a quiet start and the first chance did not arrive until just after the quarter-hour mark, Killie forward Kris Boyd heading wide from a corner.
Dundee United's Ciftci then tried his luck from a free-kick but the angle was tricky and he drove his shot just over.
However, the hosts were now looking a lot more dangerous and Ryan Gauld's effort from 20 yards out was nervously turned around the post by visiting goalkeeper Craig Samson.
Gauld then produced a superb through-ball to put David Goodwillie in on goal but the forward's powerful shot from just inside the box came back off the post.
Shortly after hitting the woodwork, Goodwillie tried his luck with a volley from fully 35 yards out and his effort flew straight into Samson's arms.
Boyd remained a threat at the other end and drew a save from Radoslaw Cierzniak, although the goal would not have stood anyway as the flag had gone up for offside.
But the hosts began the second-half firmly on the offensive and Samson denied Gauld and Goodwillie, before a well-timed challenge from Darren Barr thwarted Ciftci.
And Ciftci (55) then gave Dundee United the lead with a great goal, lashing a volley into the net from the edge of the box after Goodwillie had pulled the ball back.
The hosts continued to pile on the pressure and Gauld put a free-kick just wide of the target, before Gary Mackay-Steven embarked on a surging run and then unleashed a shot from 20 yards out which Samson kept out.
However, Kilmarnock almost scored an equaliser out of nowhere when Jackson Irvine, who had only just come off the bench, headed towards goal, only for Cierzniak to pull off a great stop.
The hosts almost made their winning margin more comfortable late on, only for Samson to pull off a good save to deny Goodwillie.
And Killie then went close twice in quick succession in the dying moments, Cierzniak tipping over a long-range Irvine effort and Rory McKenzie volleying over from the subsequent corner.