A disjointed Motherwell were run ragged in the first half and they only briefly looked like mounting a comeback after a half-time reshuffle before Stuart Armstrong, the provider of both of Ciftci's goals, ran through the heart of the visiting defence to kill off the game in the 61st minute.
Ryan Dow and substitute Brian Graham took United's tally for the season against Motherwell to 14 as the fourth-placed hosts cut the deficit to four points with three matches to play.
Motherwell could have clinched European football at Tannadice but it proved to be a day to forget for Steven Hammell, who wore the captain's armband on his 500th appearance for the club, with Lionel Ainsworth's late goal proving scant consolation.
Ciftci took just eight minutes to open his account when he started and finished a tremendous move. The striker played a first-time lay-off to Armstrong on the right wing, just inside the Motherwell half. The midfielder beat a man and returned the ball to Ciftci, who turned inside Stephen McManus and arrowed a shot into the top corner from the edge of the box.
Armstrong then cleared after Fraser Kerr cut the ball across the face of goal but that was as much as Motherwell threatened in the first half.
United, who rested teenagers Ryan Gauld and John Souttar from the start, were soon back on the attack as Ciftci played a defence-splitting pass to release Paul Paton. The midfielder lifted the ball over Gunnar Nielsen but McManus got back to head clear.
Motherwell started with defender Kerr on the right of a narrow midfield which afforded little protection for Hammell and they looked uncomfortable with the formation, resorting to playing hopeful balls forward without success.
United were causing them problems with their pace and movement and Armstrong set Ciftci clear again, but Nielsen came out to make a brilliant save.
The Faroese keeper then turned away a 25-yard strike from Gary Mackay-Steven, who almost went clean through moments later after cutting inside Shaun Hutchinson - but Keith Lasley brought him down right on the edge of the box and happily took a yellow card.
Motherwell's best hope was to keep it to one before a half-time reorganisation but they were cut open again five minutes before the break.
Centre-back Hutchinson lost out to Mackay-Steven next to the left touchline on the halfway line and United quickly exploited the space. The winger cut inside and switched play to Armstrong, whose instant cross was swept home first-time by Ciftci from 16 yards.
There was no surprise when Stuart McCall made two changes at half-time, bringing off Kerr and Henri Anier and putting on winger Ainsworth and forward Craig Moore and moving Iain Vigurs out left in a more orthodox midfield set-up.
They had two early chances but both Lasley and Ainsworth blasted over from 12 yards and United then cut the visitors open again.
Ryan Dow flicked the ball through for Armstrong to run through the middle, hold off Hutchinson and shoot into the roof of the net.
Ciftci soon fired against the outside of the post after Motherwell escaped a penalty when McManus appeared to catch Dow.
United went further ahead in the 72nd minute when Dow had all the time he needed and more to chest down Gavin Gunning's diagonal cross and fire the ball into the far corner from eight yards.
They netted again in the 81st minute when Andy Robertson threaded another ball straight through the middle for Graham to slide the ball underneath Nielsen, before Ainsworth grabbed a consolation with a deflected shot from 18 yards with three minutes left.