Elsewhere Duncan Ferguson of Everton and Wigan Athletic's Jason Roberts were sent off in a 1-1 draw at the JJB Stadium.
Middlesbrough avenged their shock home defeat earlier this season when they beat bottom-of-the-table Sunderland 3-0 while Charlton and West Bromwich drew 0-0.
Things started to go wrong at Craven Cottage for Spurs when defender Michael Dawson was dismissed in the 72nd minute for a second bookable offence.
Bocanegra then grabbed the only goal of the game in the 90th minute heading his first goal of the season from six metres following a free kick by another ex-MLS player Simon Elliott.
Spurs remained fourth on 41 points three adrift of third-placed Liverpool. Fulham climbed to 13th with 29 points.
Tempers became frayed at Wigan when Everton striker Ferguson was dismissed for violent conduct with 10 minutes to go.
Wigan forward Roberts also received the red card for a foul on David Weir three minutes later.
Everton now unbeaten in nine matches had gone in front after a ninth-minute center from Leon Osman was deflected into his own net by Wigan's recent signing David Thompson.
The home team equalized 36 minutes later thanks to a close-range volley by Paul Scharner.
Wigan on 38 points moved up one place in the table to fifth while Everton stayed 12th.
Middlesbrough beaten 2-0 by Sunderland in September went ahead against their north-east rivals when Emanuel Pogatetz headed in a free kick from Stewart Downing on 19 minutes.
Stuart Parnaby added a second goal 12 minutes later picking up a pass from Mark Viduka before drilling in a right-foot drive from 20 metres.
Jimmy Floyd Hasselbaink made certain of victory with a 20-metre shot in the 71st minute.
Middlesbrough's win lifted them to 16th while Sunderland with only two league wins all season remained rooted to the bottom.
Champions Chelsea 14 points clear of Manchester United at the top visit Aston Villa on Wednesday the same day United travel to Blackburn Rovers.
Liverpool host Birmingham City on Wednesday while sixth-placed Arsenal are at home to London rivals West Ham United.