The Scotland international was dismissed by referee Graham Salisbury in the 41st minute for violent conduct after clashing with Sergei Rebrov, who had been penalised for a challenge on Stephen Wright
West Ham had more than matched the home side before the incident and when Marlon Harewood broke the deadlock in the 59th minute, the Black Cats were really up against it.
Manager Mick McCarthy went for broke by replacing leading goalscorer Stephen Elliott with Chris Brown at the start of the second half and then sent on Michael Bridges for Marcus Stewart.
But it was all to no avail with Hammers substitute Terry Sheringham finishing off a determined break in the fourth minute of stoppage time to put paid to any hopes of the home side snatching a point.
Only the woodwork prevented the Hammers from grabbing a sixth-minute lead. Luke Chadwick found the overlapping Carl Fletcher whose rasping drive thudded against the outside of the upright with goalkeeper Thomas Myhre well beaten.
Harewood fired over the bar but the West Ham striker was guilty of a more glaring miss in the 30th minute. Allowed to go clear from an offside position, he rounded Myhre only to find the angle too tight with an open goal at his mercy.
Rebrov headed weakly at Myhre from another sweet visitors attack, while only Darren Carter tesed Stephen Bywater at the other end with a low drive that the keeper saved at the second attempt just ahead of Stewart.
Sunderland were forced onto the defensive in the second half and their back line was fully stretched when Chadwick crossed for the unmarked Harewood to score.
Gary Breen cleared off the line from Darren Powell and, with Sunderland pressing forward in vain, Harewood and substitute Bobby Zamora set up the easiest of chances for Sheringham.