On-loan striker Bruce Dyer had scored twice before Webber came off the bench to score with six minutes to go.
United swept ahead in the fifth minute with a silky three-man move. Alan Quinn rolled his corner to Steven Kabba, the little striker back-heeled to the incoming David Unsworth who cracked the ball into the top right-hand corner from 15 yards.
Former Millwall midfielder Paul Ifill hooked the ball wide after a blunder in the Lions back four and almost grabbed a second as he stretched for an Unsworth cross but his header was punched away for a corner by Paul Jones.
Millwall, prompted by midfielder Alan Dunne, soaked up the pressure and caught United on the break to grab an equaliser on 34 minutes.
Dunne swung and missed at the ball and Dyer steamed in to delicately chip the ball over Paddy Kenny from 10 yards.
The London side, growling in confidence, had United in trouble again when Tony Craig picked out former United striker Barry Hayles, but as his header spun towards Dyer, Kenny stretched so snatch the ball off his head.
Quinn saw his low drive palmed away by Jones before Millwall caught United napping as they added a second in the 55th minute.
Kenny could only push Dunne's effort back towards Dyer who headed in from close range.
Ifill clipped the bar with a long range strike, Webber had a shot deflected into the side netting and Phil Jagielka hit the bar with a fierce header before United drew level with six minutes to go.
Substitute Keith Gillespie's corner was headed down by Quinn and Webber added the finishing touch from three yards.
The game ended on a sour note when United skipper Chris Morgan was sent off in injury time for kicking out at substitute Kevin Braniff.