Ciftci scored the only goal of the afternoon with six minutes remaining after Thistle had defender Dan Seaborne sent off, with United staying in second place in the Scottish Premiership table thanks to the extra two points his spot-kick secured.
Until then the visitors had dominated for long spells, with home goalkeeper Radoslaw Cierzniak making a series of saves to keep Partick at bay.
Both sides created chances in an exciting, but eventually goalless, opening 45 minutes with Cierzniak making a fine save from Kris Doolan’s early shot.
Christie Elliott hit a shot straight at Cierzniak, but United gave as good as they got and went close midway through the period when Stuart Armstrong ran at the Thistle defence and saw his effort drift inches wide.
Scott Fox denied a rampaging Gary Mackay-Steven and Thistle came close again when Stuart Bannigan tried his luck from 25 yards, only to clear the bar by fractions.
Just like the first half, Doolan had the best early chance in the second but Cierzniak was again equal to his effort.
The home keeper came to the rescue again just before the hour Steven Lawless got on the end of an Elliott cross – he was left holding his head in his hands when Cierzniak got across to make a save low down.
Elliott was just off target from 25 yards but all of Partick’s promptings came to nothing when Seaborne was pulled up for a foul inside the box with seven minutes left to play – a red card was soon produced by referee Steven McLean just to compound their troubles.
Ciftci made no mistake from the spot and the home side were able to hold on comfortably to move back within a point of leaders Hamilton, who beat Aberdeen 3-0 on Friday night.