West Ham are 17th with 34 points while 18th-placed Hull remained on 28 with two matches remaining and a vastly inferior goal difference making their survival only the slimmest of mathematical possibilities.
Hull and Sunderland were reduced to 10 men just seconds before the break at the KC Stadium, with Jimmy Bullard missing a penalty for the hosts in the 41st minute of a bad-tempered match after Darren Bent scored in the seventh.
Hull's U.S. striker Jozy Altidore was shown the red card for apparently head-butting Sunderland defender Alan Hutton, who had thrown the ball at him after a touchline clash.
Hutton, who lay on the ground clutching his face, was also sent off and irate Sunderland manager Steve Bruce was then sent to the stands by referee Lee Probert in the second half.
"We've been in the bottom three all season really so at the end of the day you've just got to hold your hands up and say we weren't good enough," Hull chairman Adam Pearson told Sky Sports television.
Relegation will be a major blow for Hull, whose financial situation is already precarious.
"We will take it on the chin, play out the next two games and make some tough decisions over the next couple of weeks," said Pearson.
"Administration is definitely not on the agenda, there are other ways forward which are slightly less scary which we will look at first."
Heavily-indebted Portsmouth, who are already in administration and relegated, came back from two goals down to draw 2-2 at Bolton Wanderers.
Scott Parker secured the three points for West Ham with a long-range strike in the 77th minute after Wigan had taken the early lead through a Jonathan Spector own goal, heading a corner into his own net.
"The boys really gave everything," said relieved manager Gianfranco Zola.
