Although Carlton Cole had headed Alan Curbishley's men into an interval lead, Kenwyne Jones' second-half header looked to have given the Black Cats at least a point, before the Hammers bounced back off the ropes to secure a much-needed win.
Having suffered a hat-trick of Premier League defeats, the injury-hit Hammers were without both Dean Ashton, who damaged his knee ligaments at Aston Villa a fortnight ago and Freddie Ljunberg, who injured a calf on international duty with Sweden.
But there was some consolation for Alan Curbishley, who had been able to recall Bellamy and Mark Noble, while Cole came in for Henri Camara, who dropped to the bench.
Without a win in three matches, Sunderland also made a treble switch following their 2-3 defeat at Arsenal last time out as Greg Halford, Roy O'Donovan and Dickson Etuhu came in for Dwight Yorke, Michael Chopra and the suspended Paul McShane.
Straight from the kick-off, the Wearsiders' game plan was there for all to see as lone striker Jones nodded Ross Wallace's first minute free-kick over the Hammers crossbar
The Eastenders looked set for an afternoon of frustration in their quest to find a way through the Black Cats' five-man midfield shield.
But following a patient build-up, they took the lead after just nine minutes, when Hayden Mullins picked out George McCartney, whose precision centre from the left-wing was met by Cole, who outjumped both Danny Collins and team-mate Lee Bowyer, to dispatch a looping header beyond Gordon.
And after being yellow-carded for felling Collins, the busy Cole then invited the Sunderland keeper to gather his low 18-yard shot.
Jones was equally proving a handful for the Hammers defence and when he unleashed a 25-yard sizzler, the in-form Robert Green gave Steve McClaren a reminder of his capabilities with an athletic full-length stop to deny the Trinidad & Tobago dangerman.
Grant Leadbitter was booked for a reckless scythe on the battling Bowyer before Liam Miller also forced the Hammers keeper into another assured stop with a 20-yard shot, midway through the opening period.
At the other end, Matthew Etherington sent a low 18-yarder whipping wide, before the unmarked Bowyer wasted a great chance to double Hammers lead when he nodded Noble's 33rd-minute free-kick behind.
Having gone off at the break trailing to just that solitary Cole goal, Roy Keane introduced both Chopra and Anthony Stokes for the restart, in a bid to get back into the contest.
And within just six minutes, he saw his side get back on level terms, when Jones rose highest to meet Leadbitter's corner with a downward header that powered beyond the outstretched right hand of the sprawling Green.
Incredibly, having got themselves on course for one point, Sunderland then went bravely looking for all three as they subjected West Ham to some tense exchanges.
First Leadbitter let fly with a 20-yarder that Green brilliantly pushed onto his right-hand post and then the well-placed Noble hacked Etuhu's downward header off the line, before Jones nodded inches wide.
With the Black Cats showing their claws, Curbishley made a double switch as Nobby Solano stepped from the bench make his debut alongside Luis Boa Morte.
It proved an inspired choice.
For on 77 minutes, the Eastenders enjoyed a huge slice of luck when those two fresh pairs of legs galvanised Hammers into a match-winning lead after Boa Morte's left-wing cross arrived at the feet of Solano, whose shot cannoned back off the base of Gordon's left-hand upright and back into the net off the grounded keeper's heel.
That was tough on Sunderland, who endured further agony in stoppage time, when Bellamy drilled home Boa Morte's unselfish cut back to seal a welcome victory for West Ham.