Sanchez took advantage of dreadful errors from defender Wes Brown and goalkeeper Vito Mannone to ensure the Stadium of Light faithful, expecting a response following last weekend's Premier League hammering at Southampton, went home disappointed.
All eyes were on Sunderland head coach Gus Poyet's team selection following that 8-0 defeat seven days ago.
Yet Poyet largely retained faith in those players by making just two alterations, none of which came in defence as Adam Johnson and Jack Rodwell replaced Jordi Gomez and Connor Wickham.
And Arsenal, buoyed by Wednesday's last-ditch 2-1 UEFA Champions League win at Anderlecht, capitalised on their opponents' uncertainty when Brown's shocking back-pass gifted Sanchez an opener.
The visitors were in cruise control thereafter, with another miserable afternoon for Sunderland capped when Mannone failed to control Santiago Vergini's backpass in his six-yard box, allowing Sanchez to tap into an empty net in stoppage time.
Wenger, without the suspended Jack Wilshere, made three changes, with Wojciech Szczesny returning in goal having been suspended in midweek and Alex Oxlade-Chamberlain and Mikel Arteta given starts.
That meant Emiliano Martinez and Aaron Ramsey had to settle for places on the bench, where they were joined by Theo Walcott - who was appearing for the first time having spent nine months on the sidelines with a cruciate injury.
Sunderland were clearly determined to impose themselves early, although it did not take long for Arsenal to settle into a typically comfortable passing rhythm.
Arsenal's crisp play led to a first opening after 15 minutes, Danny Welbeck cutting in from the left and sending a powerful curler just over.
The home side enjoyed a good spell afterwards, only to go behind due to an individual error after 30 minutes.
Brown was the culprit, mis-hitting an attempted back-pass to allow Sanchez to race through and delicately chip Mannone for his fourth league goal since joining from Barcelona.
Not content with one, Arsenal continued to press forward with Santi Cazorla shooting just wide before Calum Chambers forced Mannone into a save.
Sunderland were dealt a blow early in the second period as injury forced off Steven Fletcher, Wickham deputising.
Wickham's introduction did not have much impact initially as Arsenal picked up where they left off, epitomised by Sanchez drawing a save from Mannone with a strike from distance.
A feistier spell ensued after that effort as Sunderland attempted to rally, Sebastian Larsson stinging the hands of Szczesny with a powerful 20-yard attempt.
That proved just a brief flurry, however, as Arsenal quickly reassumed control - albeit without really threatening a second goal.
Arsenal almost added another with 12 minutes to go, only for Welbeck to head tamely over after being picked out by the marauding Nacho Monreal.
Welbeck's miss set up a nervy ending to the game, with Patrick van Aanholt volleying wide from distance after Szczesny had left his line.
Cazorla missed a great chance to add a second when firing just over, but it mattered little as Sunderland's vulnerability reared its head again in the 92nd minute following Mannone's blunder.
