The former Watford danger man stabbed in a close-range shot after Phil Jagielka headed Keith Gillespie's free-kick into the six-yard box.
United dominated much of the game against last season's beaten play-off finalists but made heavy weather of cashing in.
And without Richard Cresswell – a target for the home side – Preston never created the menace that took them to the brink of the Premiership.
Webber impressed even before he grabbed the winner at the death.
He slipped a clever ball to Michael Tonge but the midfielder hooked his shot wide of the post then he dazzled down the left with a quick break, but after opening up the defence his low shot was wide of the post.
The home side might have been in front after 26 minutes when keeper Carlo Nash was left stranded after a dangerous cross but Neil Shipperley's goalbound prod was blocked.
After failing to create a serious threat, Preston took a shock lead after 35 minutes with their first chance.
Chris Morgan bundled over David Nugent nearly 30 yards out and Paul McKenna punished the South Yorkshire side with a stunning strike which beat Paddy Kenny.
United were deservedly back on level terms seconds before the half time whistle. Leigh Bromby's long throw was flicked on by Morgan and Shipperley hooked a close-range shot through a crowded area into the back of the net.
Danny Dichio blew a glorious chance to give Preston the points when he gave Kenny and easy save with a lame shot.
And at the other end, Jagielka made a mess of a late header after an impressive cross from Keith Gillespie before Webber had the final say.