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Jagielka was given his marching orders for pushing over David Healy in the area but the resulting penalty from Graham Alexander was saved by Paddy Kenny and United held on for three points.
The visitors started brightly and took the lead as Michael Tonge swung in a corner and Gray turned the ball in after Leigh Bromby had headed back across goal.
Preston responded well and Kenny was forced to push a well-struck Eddie Lewis drive wide of the post after the American had been put through by Richard Cresswell.
It was Cresswell who was then involved in the move that led to the referee pointing to the penalty spot after 13 minutes.
Cresswell's smart back heel put Healy through on goal, but the striker could not keep his balance as Jagielka caught him from behind.
Referee Chris Foy deemed Jagielka's offence serious enough to warrant the red card, but United escaped immediate damage as Kenny punched away Alexander's poor penalty.
United were aggrieved at the award of the penalty and the sending-off, and Foy had to book Chris Morgan moments later after a foul on Healy.
Chris Lucketti went close to an equaliser just after the half hour when he headed narrowly wide from a Healy corner.
Healy also had two chances to level just before the break, Bromby blocking his first shot and the second sailing over from an Alexander cross.
Preston struggled to make headway after the break, failing to create a meaningful opportunity until Lewis curled a free-kick onto the top of the crossbar after 65 minutes.
United almost doubled their lead three minutes later when Alan Quinn diverted a low Tonge effort but the ball bounced wide.
Preston twice had appeals for handball against Morgan in the area turned down as they stepped up the pressure late on. Foy ruled on both occasions that contact had been accidental.
United could have made the win safe six minutes from time but Andy Lonergan produced a fine reflex save from a deflected Ashley Ward shot.
The home side dominated possession throughout the four minutes of injury time but could not find a way through the Blades rearguard.