Bobby Zamora bounced back to goalscoring form with a hat-trick to give Albion an extraordinary victory.
The Seagulls led three times through Gary Hart and a Zamora double, the first a penalty.
Cambridge hit back within minutes on each occasion, via Shane Tudor, Luke Guttridge and a Paul Wanless spot kick.
The visitors were reduced to ten men before Wanless took his penalty, Andy Duncan seeing red for an incident off the ball.
Albion capitalised on their numerical advantage, Zamora completing his fourth hat-trick for the club with a minute remaining.
It was a wonderful way for the Seagulls' young hotshot to finish a four-match famine and it gave Peter Taylor's promotion chasers a vital first victory for six games against the side with only one away point all season.
Hart put Albion ahead on 25 minutes, rifling his third of the season when Danny Cullip headed a Nathan Jones throw into his path.
Tudor raced away to put Cambridge level on 27 minutes, only for Zamora to put Albion back in front with a 50th minute penalty.
He had a spot kick saved against Preston in the FA Cup on Tuesday, but the 21-year-old made no mistake this time after referee Phil Prosser had originally awarded a free-kick on the edge of the area.
Cambridge were level again within four minutes, Luke Guttridge converting the rebound when Simon Royce marred his home debut by pushing a long range shot from Paul Wanless straight into his path.
Zamora cut inside to finish a cross on 75 minutes from Robbie Pethick, one of three second half substitutions made by Taylor.
Incredibly Cambridge restored parity once more on 80 minutes. Pethick was adjudged to have fouled sub Alex Revell and Duncan was dismissed following some argie bargie on the edge of the box before Wanless sent Royce the wrong way from the spot.
The drama was not over, Zamora bringing a Withdean crowd of 6,475 to its feet with a header from a Hart cross on 89 minutes, his 22nd of the season.
There was even better news for the Seagulls, with promotion rivals Bristol City, Stoke and Brentford all losing at home.
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