An eventful match turned on a straight red card just before half time for Brighton striker Gary Hart. Referee Joe Ross sent him off for elbowing Trond Andersen in an off-the-ball incident.
Brighton made a flying start, Paul Brooker driving them ahead after only three minutes. Wimbledon keeper Kelvin Davis parried a Simon Rodger corner into the path of the former Fulham winger and Brooker slotted his third of the season from 12 yards.
Connolly equalised against the run of play on 39 minutes, escaping his marker to head in Gareth Ainsworth's right-wing cross.
Wimbledon made their extra man count on 48 minutes. German youngster Moritz Volz, making his debut on a month's loan from Arsenal, exchanged passes with Damien Francis to beat veteran Dave Beasant with a low drive.
The 43-year-old Beasant celebrated his home debut for Brighton by saving a 54th minute penalty against his former club. He dived to his right to keep out Neil Shipperley's spot-kick, after Shipperley had been fouled by Brighton skipper Danny Cullip.
Connolly put the match beyond Brighton 11 minutes from time. He held off Cullip to slip the ball past Beasant from close range.
Bobby Zamora latched on to a pass from sub Graham Barrett to slot his eighth of the season four minutes from time, but the result means Brighton are still three points adrift at the foot of the table.