Saints had taken a first-half lead through Jack Ross before Feeney levelled from the penalty spot and Billy Mehmet also converted from 12 yards to restore the visitors' lead.
But United's determination paid off and goals from Prince Buaben and Feeney late on allowed the Tannadice club to claim the win and leave the Buddies reeling.
United manager Craig Levein wrote off his side's shock 4-0 defeat to Motherwell on Sunday as nothing more than a bad day at the office and was confident they would be back on top form for the visit of Saints.
In fact, he kept the faith with almost the same team, Bauben the only replacement for Scott Robertson, who had been told he could be out for the rest of the season with a groin problem.
While the hosts attempted to haul themselves back into contention for third spot, survival was the main priority for a Saints side who headed into this game eight points clear of rock-bottom Inverness but knowing the relegation issue was far from clear-cut.
The warning signs were there early on for the home side, as St Mirren hit the woodwork twice in the opening 10 minutes.
The first chance arrived with just two minutes on the clock when Andy Dorman raced onto a Craig Dargo flick and unleashed a ferocious 25-yard drive which clipped the inside of the post before the danger was cleared by the United defence.
Mehmet then rattled the upright from close range after being set up for the shot by Stephen McGinn, before Dargo's rebound effort was inadvertently blocked by Mehmet.
United's first chance fell to Jon Daly, who was picked out by Craig Conway's cross from the left, but he blasted over from a few yards out.
They were left ruing that missed opportunity when Saints took the lead with 17 minutes gone in spectacular style. Dargo slipped a pass through to Ross, who sent a lovely, swerving effort into the back of the net from 25 yards.
Saints then squandered an opportunity to add to their advantage before the break when the ball broke to Hugh Murray and he blasted over from just outside the six-yard box.
United looked more dangerous after the break and Conway was not too far away with a powerful shot which dipped narrowly over the crossbar.
They continued to push forward in numbers but largely found themselves frustrated by an impressive defensive display from Saints.
Any hopes of a comeback could have suffered a setback when Lee Wilkie appeared to handle in the box but the incident went unnoticed by referee Stevie O'Reilly.
With just over an hour gone, the Tangerines then made their first change of the game when Daly was withdrawn in favour of Francisco Sandaza.
United were back on level terms with 71 minutes gone when Wilkie was fouled on the box by Franco Miranda and Feeney lashed home from the penalty spot.
But Saints were able to restore their lead just two minutes later, with Wilkie involved again when barged into Dargo and the referee pointed to the spot once more.
Mehmet stepped up for the pressure kick and kept his cool to convert from 12 yards.
Just when Saints must have thought they were returning to Paisley with maximum points, they were hit by a double sucker-punch.
Buaben restored parity with 83 minutes on the clock when his 25-yard effort was helped into the back of the net by goalkeeper Mark Howard, before Feeney met a Sandaza ball across the face of goal to slot home at the back post three minutes later.