The win turned up the pressure on Manchester City ahead of their trip to Liverpool on Sunday.
The contest was far from a classic, defined instead by a bitty, stop-start rhythm that leaned heavily on set-pieces and territorial control rather than creativity.
Yet it was another example of Mikel Arteta's pressing-focused, highly structured approach paying dividends, with Arsenal largely dictating play in and around Sunderland's penalty area.
Sunderland deserve credit for disrupting Arsenal's fluency and preventing long spells of sustained pressure, particularly in the early stages.
Kai Havertz, preferred to Viktor Gyokeres from the start, headed wide inside the opening minute, while Trai Hume diverted a dangerous Noni Madueke cross over his own bar.
Declan Rice later dragged a shot narrowly wide as Arsenal probed without finding a breakthrough.
The decisive moment of the first half came just before the interval. Omar Alderete was caught in possession by Madueke, allowing Leandro Trossard to work space and tee up Martín Zubimendi, who found the net via the inside of the post.
Arsenal doubled their advantage midway through the second half after Nordi Mukiele surrendered possession. Trossard again played a key role, slipping in Havertz, whose unselfish square pass was calmly converted by substitute Gyokeres.
The striker then added a third, capitalising on a Reinildo error before finishing off an injury-time break led by Gabriel Martinelli.