After an even first period, the visitors stepped up the pressure after the break but could not find a way past a resolute Hearts defence.
It was a no-scoring game but at the same time far from dull. The visitors' finesse in the final third came up against a spirited Hearts rearguard that worked tirelessly.
United went the closest through Ciftci after the break but his effort came back off the post.
The Tayside outfit's controlled start had Hearts pegged back during the early stages but it was the hosts that registered the first shot on target after seven minutes.
Jason Holt wriggled free in midfield but Radoslaw Cierzniak got down well to his bouncing effort.
Hearts winger David Smith's inswinging free-kick then caused problems but the Polish goalkeeper made a decent block in a crowded box.
United responded with their first opening of the game after 11 minutes when David Goodwillie crashed a shot into the side-netting after a forceful run from Ciftci.
The visitors continued to look better in possession but Hearts were more dangerous on the break, and a long-range Smith effort worked Cierzniak.
United then upped the tempo and created a hat-trick of chances in quick succession. Stuart Armstrong shot wide from 18-yards before firing another effort over following neat build-up play by John Rankin and David Goodwillie. Midfielder Rankin then had a stinging drive palmed away by goalkeeper Jamie MacDonald.
It seemed a matter of time before the opening goal would arrive for United.
Ciftci converted a well-executed finish from inside the box but Goodwillie had already been penalised for a push.
The visitors were then left incensed after having a goal ruled out by an assistant referee.
Callum Paterson's long throw caught out the goalkeeper to leave Dylan McGowan with a simple tap-in but a push in the area was spotted.
Before the gripping half was out, MacDonald made a great close-range block to deny Keith Watson after a threatening United counter. The second period began in the same manner as United continued to press.
A Hamill slip in midfield allowed United forward Ciftci the chance to unleash a powerful shot that MacDonald was happy to beat away.
Rankin then should have done better with a left-footed drive that was straight at the Hearts goalkeeper.
Hearts were on the ropes and the upright came to their rescue in the 66th minute. Armstrong out-muscled Dylan McGowan on the flank and his cross found its way to Ciftci on the edge of the box but the Turkish player's first-time effort from 18 yards came back off the post.
Hearts were full of fight but for much of the game they offered little in an attacking sense. Wilson got his head to another Walker corner but again the ball drifted wide.
A captivating ending saw both teams look dangerous on the break but neither could provide the killer touch.