Gus Poyet's side went down to nine men and the manager stormed down the tunnel before re-emerging to lead sarcastic applause of referee Craig Pawson.
Romain Vincelot was dismissed for foul and abusive language after six minutes and Ashley Barnes followed on 12 after an altercation with Chris McCann.
The Seagulls' resistance was broken in the 32nd minute when Kieran Trippie's shot found the net.
Middlesbrough ended Cardiff's nine-match unbeaten league run as they came out on top 3-2 in a five-goal thriller in Wales.
Boro's Bart Ogbeche opened the scoring with the aid of a deflection seconds after Cardiff were denied what looked like a stonewall penalty when Jason Steele appeared to foul Kevin McNaughton.
But justice was served when Ben Turner powered home to level and Aron Gunnarsson gave the Bluebirds the lead shortly before the break after a superb run and back-heel from Kenny Miller.
Scott McDonald equalised after Justin Hoyte beat the Bluebirds' offside trap and Faris Haroun volleyed home on 76 minutes to leapfrog their opponents into third spot.
Papa Bouba Diop took advantage of a free header to give the Hammers the only goal of the game after six minutes.
At the foot of the table, rock-bottom Coventry lost 1-0 at Peterborough to Emile Sinclair's goal, while Bristol City drew 0-0 with fellow strugglers Nottingham Forest after David James turned back the years to deny Steve Cotterill's side a much-needed three points.
Elsewhere, Billy Sharp scored twice as Doncaster came from behind to beat Leicester 2-1 after David Nugent gave the Foxes the lead, while Simon Church's second minute goal for Reading proved enough to down Leeds 1-0.
Robert Koren had a hand in both Hull goals as they beat Millwall 2-0. The Slovenian's cross on 54 struck the luckless Jack Smith and bounced home before Koren volleyed a second with 10 minutes remaining.
Keith Andrews' header saw Ipswich edge past Derby 1-0, while Blackpool v Watford ended goalless.