The Gunners went into the match having beaten Sevilla in midweek, though it had been back-to-back domestic defeats after a Carabao Cup exit to West Ham and a controversial loss to Newcastle.
There was to be no hat-trick, or indeed controversy, at the Emirates Stadium, as Arsenal maintained their unbeaten start to the season on home soil in relatively comfortable fashion to move level on points with Manchester City, for now, at the top of the Premier League.
Leandro Trossard opened the scoring just before the break, and while Josh Brownhill levelled in the second-half, William Saliba's header got the Gunners back in front almost immediately. Oleksandr Zinchenko's superb finish gave Arsenal real control, ensuring a late red card for Fabio Vieira did not make things too nervy.
Trossard has scored six goals for Arsenal this season and all of those have been assisted by Bukayo Saka. The Englishman, fit to start despite picking up a knock in midweek, looped a header up and Trossard bundled it home from close range, colliding painfully with the goalkeeper and the post in the process.
Brownhill equalised shortly after the break to briefly stun the Emirates, his deflected strike flying past David Raya, but the Clarets were on level terms for just three minutes.
Arsenal had looked dangerous from set-pieces all afternoon and they finally made one count, as Trossard clipped a corner into the six-yard box and Saliba rose highest swiftly restore the Gunners' advantage.
Burnley's defending from corners again let them down as Arsenal moved further in front with 15 minutes remaining. The Clarets were fortunate not to turn the ball into their own net, as it rebounded off the bar from yet another corner, but Zinchenko was there to acrobatically find the top corner from the rebound with a wonderful scissor-kick finish.
Fabio Vieira, a second-half substitute, was shown a straight red card late on, after catching Brownhill with a late and high challenge, but Arsenal had enough of a cushion by then to see the match out without any further drama.