Henderson guided home Asamoah Gyan's pull-back in the 34th minute to claim his first goal of the season and earn Sunderland a win that takes them up to seventh, level on points with Bolton above them.
Victor Obinna came closest to snatching a point for West Ham with a 79th-minute effort which hit the outside of the post, but the Black Cats were good value for the victory.
Steve Bruce has spent much of the season to date pleading with his midfielders to help out strikers Darren Bent and Gyan on the goals front, and Henderson's contribution will have been as welcome to him as it was to the bulk of a crowd of 36,940 on a bitterly cold afternoon.
The Hammers arrived on Wearside still basking in the glory of their midweek Carling Cup demolition of Manchester United, but knowing the revival they launched in the league with last weekend's 3-1 win over Wigan was the overwhelming priority.
Avram Grant's men had climbed from the foot of the table without kicking a ball as a result of Wolves' defeat at Blackburn 24 hours earlier, and as the only side to have won at the Stadium of Light this season - a 2-1 Carling Cup success in September - they had high hopes of extending a run of six games which had brought just one defeat.
However, that home record has been jealously guarded by Bruce's men and, having lost just their third league game of the campaign at Wolves last Saturday, they were determined to improve it further.
The hosts started the game far brighter fashion, and their cause might have been helped had referee Martin Atkinson ruled that Luis Boa Morte's two-footed seventh-minute challenge on Kieran Richardson was worthy of a red rather than a yellow card.
Skipper Lee Cattermole forced the first save of the game from Robert Green with a long-range 15th-minute effort which skidded trickily off the turf in front of the keeper, although opposite number Craig Gordon had to get his positioning right to claim Obinna's free-kick seven minutes later.
But as the first half wore on, Sunderland started to threaten on a more regular basis and, after Bent had warmed Green's hands with a dipping long-range shot, they forced their way ahead 11 minutes before the break.
Gyan, back in the starting line-up in place of Bolo Zenden, found space down the right before squaring for Henderson to guide the ball deftly past Green.
Danny Welbeck clipped the bar with a curling shot two minutes later, but the Hammers might have got themselves back on to level terms with 44 minutes gone.
Jonathan Spector, who scored twice against United, embarked upon a surging run which took him deep into the Sunderland penalty area, but he lost his balance as he shot under pressure from Anton Ferdinand and stabbed his effort just wide.
The Hammers returned in determined mood and might have wiped out Sunderland's lead within four minutes.
John Mensah slipped as Carlton Cole turned on Obinna's pass and drilled a left-foot shot across Gordon, but unfortunately for him, just wide of the far post.
The visitors were enjoying their most dominant period of the game, but despite Sunderland's carelessness in possession, were finding clear-cut chances at a premium.
Gyan spooned a 57th-minute effort high over the crossbar as he failed to make the most of Richardson's lay-off, but as Kieron Dyer started to make his presence felt, the impetus was very much with the Londoners.
Richardson forced a 64th-minute save from Green, who had to be at his best to turn away Gyan's stinging drive two minutes later, but the Hammers might have snatched a point with 11 minutes remaining.
Obinna picked up possession inside the box and blasted towards Gordon's bottom right-hand corner, only to see the ball clip the outside of the post and drop to safety.
However, Sunderland should have killed off the Hammers once and for all with five minutes remaining.
Substitute Steed Malbranque went into a 50-50 with Green and saw the ball come back off the keeper and fall to Welbeck, only for James Tomkins to get in a vital block as the fans behind the goal waited for the net to bulge.