Goals from Paul McGowan and Steven Thompson had put St Mirren in command but the home side threw off their lethargy in the final quarter to draw level courtesy of substitutes Brian Graham and Stuart Armstrong.
Suddenly, Marian Kello's goal was under siege and Ciftci pounced in the third minute of added time to seal a thrilling, if highly improbable, victory.
Thompson had a decent chance but headed wide from 10 yards as the visitors began with plenty of attacking intent.
Their early endeavour was rewarded when McGowan (20) headed his third goal of the season, latching onto Marc McAusland's free-kick.
Thompson was a constant threat to the hosts and, when Gavin Gunning when tried to clear John McGinn's cross, the ball flew off Thompson (40) into the net his 14th of the season.
Dundee United striker Farid El Alagui fired over the top on the stretch but it was a rare threat from a lacklustre home side.
Indecision in the St Mirren defence presented Ryan Gauld with a glorious chance to half the deficit, but the United youngster failed to hit the target from 12 yards.
Graham did better when he ignored St Mirren appeals for offside to fire past Kello (79) from close range.
Suddenly the force was with the home side and Armstrong's assured right-foot finish brought the equaliser (84).
Panic swept over the St Mirren rearguard and the pressure duly told when Kello spilled the ball and Ciftci swept in from close range, sparking wild celebrations both on and off the pitch.