They are 11 points behind leaders Chelsea while much-changed Sunderland remain bottom.
Van Persie netted his third goal of the week, Henry added the second and then killed Sunderland's brief hopes of an unlikely revival.
Arsenal have won all their six Premiership games at Highbury and that home record has kept them in touch with the leading group.
The Gunners often had problems after Champions League matches in the past but this season they have won each of their four games after European nights.
Arsenal's second string triumphed 3-0 at Sunderland in the Carling Cup last month. Van Persie scored in that game too. Today their stars rarely needed to move out of cruise control.
Jens Lehmann returned after back trouble for the Gunners, Cesc Fabregas replaced Mathieu Flamini in midfield and two-goal midweek hero van Persie started up front with Henry.
Black Cats boss Mick McCarthy made six changes after his side's 4-1 home defeat by Portsmouth last weekend.
Eighteen-year-old youth product Ben Alnwick made his Premiership debut in place of Kelvin Davis in the Sunderland goal. He can be pleased with his display, but his colleagues gave him scant protection.
Former Waterford midfielder Daryl Murphy, 22, made his first Premiership start too. Justin Hoyte, on loan from Arsenal for the season, missed the game as part of the deal. Julio Arca, George McCartney, Stephen Wright and Christian Bassila were all sidelined with injury.
Sunderland looked disjointed. They began with Gary Breen playing as the anchor in front of three one-paced centre-backs. They tried to protect them with an offside trap which caught Henry three times in the first five minutes but inevitably, the trap was later sprung.
Sunderland left Andy Gray as a lone striker with occasional support from Jonathan Stead. Gray cut a forlorn figure and both were substituted at half-time.
Arsenal soon pressed. Alan Stubbs' error presented Jose Antonio Reyes with an early chance, but the Spanish winger shot into the side-netting.
Van Persie broke the deadlock in the 12th minute, nipping between Stubbs and Nyron Nosworthy to chest down Sol Campbell's long pass and strike a trademark left-foot finish. Alnwick had no chance.
Stephen Caldwell flicked a half-cleared corner across the box in a rare Sunderland attack. A set-piece looked their only hope of threatening Lehmann.
Arsenal continued to dominate, though Henry was caught offside twice more. Sunderland, confidence at rock bottom, kept inviting pressure by giving the ball away.
Alnwick saved from van Persie and Fabregas shot over as Sunderland failed to clear a corner. In between, Henry added the second, nine minutes before half time. The move was simple and direct - Lauren beat the offside trap and crossed low to the far post where Henry prodded home.
McCarthy sent on strikers Stephen Elliott and Anthony Le Taillec for the second half.
Sunderland gained two successive corners before Arsenal soon took charge again. Reyes' flick sent van Persie away but the Dutchman shot over. Henry freed Gael Clichy on the left and the full-back skewed his centre out of play. Reyes sent van Persie through again but another offside flag rescued Sunderland.
Arsenal carved the visitors open almost at will. Van Persie swivelled on the edge of the box and smashed a right-foot shot inches wide before Alnwick foiled van Persie after the Dutchman had played a one-two with Henry.
Van Persie returned the favour, finding Henry with a clever pass. Arsenal's record scorer took the ball on his chest with his back to goal - and his overhead kick bounced off an upright.
Dennis Bergkamp replaced van Persie to make his 300th Premiership appearance for the Gunners. It all seemed so easy for them.
Their complacency was suddenly jolted by a Sunderland goal. Caldwell headed down a 75th-minute corner and Stubbs poked the ball past Lehmann.
Henry settled any home nerves with eight minutes left. He controlled Fabregas' pass, slipped the ball through Caldwell's legs and aimed a right-foot shot beyond Alnwick.
The young keeper saved well from Bergkamp with time running out. He shouldered no blame for Sunderland's defeat.
MAN OF THE MATCH: Robin van Persie (Arsenal) - Scored another fine goal and looked full of menace as the Gunners strolled to a comfortable victory against a seemingly doomed Sunderland side.