On-loan Stoke striker Bruce Dyer notched a clinical double to cancel out David Unsworth's early opener and put the Lions on course for a shock victory.
But Webber was on hand to fire the ball home from close range in the 84th minute to extend the Blades' unbeaten home record to 10 matches.
United began strongly and were rewarded with Unsworth's fifth-minute opener, the former Everton defender thrashing home Alan Quinn's cross following a well-worked short-corner routine.
Neil Warnock's side wasted no time in attempting to extend their lead and former Millwall winger Paul Ifill quickly emerged as their most influential player.
The £800,000 summer signing from the New Den collected the ball on 11 minutes before teasing and tormenting the visiting defence.
The tricky wideman engineered a shooting chance but could only drag a left-footed effort narrowly wide.
The Blades, who romped to a 4-0 victory at the New Den little more than a month ago, were dominant and came close to doubling their lead after 19 minutes.
Unsworth, enjoying a new lease of life at Bramall Lane following his release from Portsmouth at the end of last season, delivered a delightful cross from the left flank.
It was met by Vincent Pericard, who planted a firm header goalwards but could only watch in agony as Lions goalkeeper Paul Jones produced a fine reflex save to deny the on-loan Portsmouth striker.
But with 25 minutes gone, the Lions began to bare their teeth as Alan Dunne collected the ball 25 yards from goal and curled a superb effort just wide.
United continued to dominate possession, but, after failing to make it pay, Millwall levelled after 34 minutes.
A rare break from the visitors culminated in Barry Hayles firing in a shot which fell to Jermaine Wright, and the on-loan midfielder teed up Dyer to sweep the ball home from 12 yards.
The Lions almost stole ahead on the stroke of half-time when Hayles' header drew a fine save from United goalkeeper Paddy Kenny.
But with 55 minutes gone Millwall edged ahead as Dyer nodded home to stun the Bramall Lane faithful.
The Lions were the last side to collect maximum points at Bramall Lane following their 1-0 victory in the Steel City last April.
But United, sensing a shock defeat, reacted positively to going behind and Ifill came close from distance with a superb effort.
The former Lions star suffered further agony on 64 minutes when he smashed a 35-yard effort against the bar with goalkeeper Jones beaten.
Millwall began to defend like demons, but they could not prevent Webber from diverting Quinn's header home from six yards to ensure they remain a point clear of Reading at the top of the Championship.
United suffered a blow in the last minute as skipper Chris Morgan was dismissed for violent conduct while Millwall collected five bookings during a feisty encounter.