Gus Poyet’s side fared considerably better than in their last outing – when they were hammered 8-0 by Southampton – but were once again left to count the cost of defensive mistakes.
Brown, one of their seasoned performers, got himself in a horrible mess on the half-hour mark.
With the ball caught under his feet, he tried to bundle back to Mannone but only succeeded in presenting Sanchez with a clear run on goal – with the talented Chilean keeping his composure to casually dink over the advancing Sunderland goalkeeper.
Arsenal were once again far from their best but wrapped up the points in the dying seconds when Mannone took a heavy touch inside his own box and Sanchez gratefully accepted the gift to rattle into an empty net.
The home side’s humiliation on the south cost last weekend had cast long shadows and head coach Poyet sent his team out demanding a reaction, although that was always going to be easier said than done against an Arsenal team packed with talent, although depleted by injury and suspension.
However, the Uruguayan could only look on helplessly as his players initially struggled to shake off the trauma of their Southampton nightmare.
The Gunners, predictably, retained possession with ease as Mikel Arteta and Mathieu Flamini supplied the excellent Sanchez, Santi Cazorla and Alex Oxlade-Chamberlain ahead of them to repeatedly stretch the home defence.
By contrast, the Black Cats at times treated the ball as if it were a live hand-grenade as they retreated ever deeper towards Mannone.
However, for all their early dominance, the visitors struggled to create clear openings with former Sunderland loanee Danny Welbeck sending a swerving, dipping 15th-minute effort on to the roof of the net after Sanchez had fired wide from distance.
Poyet’s men only rarely managed to venture into enemy territory with the left flank their only real outlet, and while winger Will Buckley tested defender Calum Chambers on several occasions, it was full-back Patrick van Aanholt who forced an important 25th-minute block from Per Mertesacker after running on to Sebastian Larsson’s pass.
But it was Mertesacker’s clearance which indirectly led to the opening goal.
Brown looked to have the ball under control just inside his own half and turned neatly away from Sanchez in order to play it back to Mannone.
However, his disastrous miskick allowed the Chilean to run through on goal and delicately chip the onrushing keeper.
Cazorla and Arteta both went close as the Gunners looked to kill the game off before half-time, although the home side managed to escape further damage.
Whatever Poyet said during the break appeared to have an effect as his players returned in far more determined mood and set up camp much higher up the pitch.
He was forced into a 50th-minute reshuffle when lone striker Steven Fletcher limped off to be replaced by Connor Wickham, and the newcomer arrived with his team enjoying their most productive period of the game to that point with midfielder Jack Rodwell forcing a save from Wojciech Szczesny with a firm header two minutes later.
For the first time in the game, the Arsenal rearguard found itself under concerted pressure, although the home side’s frailty at the back invited further pressure with Brown almost serving possession up to Chambers before Van Aanholt’s aimless clearance allowed Sanchez to test Mannone from distance.
Larsson warmed Szczesny’s hands with a 65th-minute drive from 25 yards and substitute Jozy Altidore looped a header towards goal from Van Aanholt’s inviting cross with 14 minutes remaining.
However, the United States international fluffed his lines two minutes later when, having been picked out with a raking long pass by fellow substitute Jordi Gomez, he scuffed a volley harmlessly across the penalty area.
Szczesny very nearly handed Van Aanholt on 81st-minute opportunity to level when, fearing he was about to step outside his area, he headed the ball straight to the full-back wide on the left, although the Dutchman’s long-range effort sailed wide of the far post with Mertesacker racing back to cover for his keeper.
But disaster struck at the death when Mannone failed to control Buckley’s back-pass and Sanchez added a second from close range.
Phil Thompson’s verdict
It was two horrendous mistakes and for all the possession Arsenal had in the game, certainly in the first half, they have got to be having more attempts on target. This was an extremely nervous Sunderland side and for all the possession Arsenal had they should have won this more comfortably.
The goals were absolutely shocking. When they analyse them on Sunday morning they will see them and think ‘why?’ Wes Brown had plenty of time on the ball and yet he let Sanchez, who was Arsenal’s best player, get away. The second one was in injury time and they just had to clear their lines. Mannone couldn’t sort his feet out and hit it straight to Sanchez. Two mistakes cost them.