The Frenchman, playing in the final Premier League game of his loan spell, volleyed home from Andrey Arshavin's injury-time cross to complete a comeback which had begun when Aaron Ramsey had cancelled out James McClean's 70th-minute opener.
However, the visitors were unhappy with the Irishman, who picked up a loose ball with defender Per Mertesacker writhing on the ground after catching his studs in the turf and fired past keeper Wojciech Szczesny.
It proved a difficult afternoon for the Germany international, who survived first-half appeals for a penalty from the bulk of a crowd of 40,312 in a hard-fought encounter.
Sunderland went into the game defending a five-game unbeaten run and having won nine of the 13 games they had played under manager Martin O'Neill, but knowing they faced one of the toughest tests of that sequence of fixtures.
Arsenal's 7-1 demolition of Blackburn last weekend had not exactly set the alarm bells ringing, but the Black Cats knew they would have to be at their very best to get anything out of the game.
They left the pitch at half-time all square, but firmly believing they should have been in front, not because they dominated the opening 45 minutes, but because they felt they had been done a major injustice.
The Gunners enjoyed the better of the possession, although it was their hosts who created the first real opening when McClean headed Sebastian Larsson's near-post corner over the bar with 11 minutes played.
But with Mikel Arteta anchoring an Arsenal midfield in which Tomas Rosicky ahead of him linked with Alex Oxlade-Chamberlain and Theo Walcott at every opportunity, the visitors were a threat throughout.
However, while they were forced to soak up pressure for much of the first half, the Black Cats rearguard was in no mood to be punctured and 28-goal striker Robin van Persie was kept relatively quiet by his standards with Michael Turner in particular impressive.
The visitors' best chances of the half both fell to England international Walcott, who fired across goal from Van Persie's 23rd-minute pass, and then volleyed harmlessly over on the half-hour from Alex Song's cross.
However, the game erupted into controversy six minutes before the break when O'Neill's men thought they should have been awarded a penalty.
Mertesacker controlled Jack Colback's cross on his chest, but then saw the ball rear up off the turf and hit his arm.
But as the home fans appealed as one, referee Neil Swarbrick waved play on.
The official's stock fell further with the home fans with a minute of the half left to play when he booked Fraizer Campbell for a foul on Van Persie, and he headed for the dressing room at the break to a predictably hostile chorus.
Arsenal controlled the opening stages of the second half too, although again without causing too many problems for the home side.
However, it was Sunderland who went close seven minutes after the restart when, after Craig Gardner's shot from a free-kick move had been blocked, the ball fell to defender John O'Shea, who blazed high over.
But the traffic was largely one way and as Sunderland's efforts to clear their lines grew increasingly desperate, they found themselves retreating deep into their own half.
Sixty-one minutes had elapsed without either keeper having to make a save of any note, but Wojciech Szczesny was called upon twice within as many minutes to deny Gardner as the home side threatened to turn the tide.
First the Pole got down well to turn away the midfielder's left-foot drive, and he then needed to be even more resolute to repel the same player's dipping volley.
Gunners boss Arsene Wenger decided enough was enough with 24 minutes left when he replaced Oxlade-Chamberlain with loan signing Henry, but his side fell behind in unfortunate circumstances within four minutes of the Frenchman's arrival.
Mertesacker caught his studs in the turf as he attempted to shepherd a harmless ball back to Szczesny, and as he collapsed to the floor in agony, McClean ran clear to fire past the keeper for his second goal in as many league games.
The Germany international left the field on a stretcher to be replaced by Ramsey, who needed just three minutes to announce his arrival in style.
A loose ball broke to the midfielder 20 yards out and he swivelled to send in a low shot which hit both posts before crossing the line with Mignolet helpless.
But there was more to come as the game entered stoppage time when Henry timed his run to perfection to turn fellow substitute Arshavin's cross past Mignolet.