The result meant the Ayrshire outfit are the only side in the Scottish Premiership still searching for their first win of the season after fellow strugglers St Mirren triumphed at Hearts.
The Saints victory also saw them leapfrog Killie, who slipped to 11th in the table.
Kilmarnock were without on-loan Michael Gardyne, who was banned from playing against his parent club and missed the visit to Tannadice.
United - unchanged from last week - had Gary Mackay-Steven and Gavin Gunning back from injury and suspension respectively but both had to settle for a place on the bench.
The match was just five minutes old when Ismael Bouzid picked up the first booking after clattering into Paul Paton.
He was followed into referee Willie Collum's book by team-mate Sean Clohessy for a challenge on Cifti, who sent the resultant free-kick just over from a tight angle.
United were forced to make their first change on 27 minutes when Keith Watson was forced out of the action with a bloodied face and was replaced by Gunning.
David Silva then tried his luck for the visitors with a drive that was deflected wide for a corner that Killie failed to capitalise on.
The United forward also looked dangerous after the break, forcing two quick-fire saves from Craig Samson as the home side tried to crank up the pressure.
Ciftci then found himself through on goal but was denied the sight of the net bulging by a timely block from Darren Barr.
However, the Turk was celebrating after 56 minutes when he fired the Tangerines into the lead in impressive style.
Goodwillie delivered the cross from the left and Ciftci unleashed a lovely volley from the edge of the area that left Samson with no chance.
United could have doubled their advantage when Gauld presided over a free-kick 30 yards out, after being fouled by Manuel Pascali, but rifled inches past the upright.
Substitute Mackay-Steven then embarked on a surging run past several Killie players only to let himself down with a tame shot that was comfortably claimed by Samson.
Jackson Irvine was thrown into the action for Killie and almost grabbed the leveller when his header flashed just wide, before picking up a caution, in what was an eventful first couple of minutes on the park.
Goodwillie could have all but put the result beyond doubt with five minutes to go with a powerful strike that was well-saved by Samson.
The Killie keeper was on top form again to deny Ryan Dow at the near post, before Radoslaw Cierzniak clawed another Irvine effort to safety as United held on for the win.
- Sports & Recreation
- Craig Samson
- Michael Gardyne