Preston, last season's defeated play-off finalists, were beaten 3-0 at home by Reading last Saturday before learning that the striker had rejected the offer of a contract extension.
Cresswell scored 19 times last season but was omitted from Preston's squad for this match and may complete a move to Bramall Lane this week. He was previously the subject of a failed bid from Neil Warnock and the recent sale of Andy Gray to Sunderland means that the club has both increased resources and the urgent need for a replacement.
On the pitch it appeared that Preston had earned the point their resolute performance just about deserved after Chris McKenna's expertly flighted free-kick had given them an unlikely first-half lead.
But Neil Shipperley equalised for the Blades just before the break and a draw appeared inevitable until Webber forced the ball home from close range a minute into injury time.
"They were two great times to score goals," said Warnock. "We said if we kept going until the end that we'd get a chance to win the game and we did.
"We looked strong. We're getting better and some of our players are still not at their best yet."
The South Yorkshire club had dominated the opening period until McKenna struck with a delightful right-footer from almost 30 yards that sailed into Paddy Kenny's top-left-hand corner.
Sheffield's equaliser arrived when Leigh Bromby's long throw was flicked on by Chris Morgan. Shipperley - whom Cresswell seems likely to replace - hooked the ball over his shoulder and in off the far post.
Despite their defensive outlook, Preston still posed an intermittent threat in the second half. That much was proved by the promising David Jones, who set up Danny Dichio for what should have been a simple finish.
Jones' fine through ball was lofted over Morgan's head but Dichio side-footed gently into Kenny's arms - and was promptly substituted.
Despite three attacking substitutions, Sheffield did not look dangerous until Phil Jagielka headed across goal, leaving Webber with the simple task of poking the ball home from a yard.
"We didn't get what we deserved," said Billy Davies, the Preston manager. "We controlled most of the second half." Davies, however, is resigned to losing Cresswell. "You don't need to be a rocket scientist to know why I left him out," he said.Reuse content