Two first-half goals set the platform for the Gunners' first top-flight win since 1 November.
Alexandre Lacazette sent goalkeeper Edouard Mendy the wrong way from the penalty spot and Granit Xhaka curled in a superb free-kick 10 minutes later to put Arteta's side in control.
Bukayo Saka's cross then dropped into the top corner early in the second half to put the game beyond the visitors.
Tammy Abraham scored from close range to make it a nervy final five minutes for the hosts and Jorginho then saw his weak penalty saved by Bernd Leno.
But it was an otherwise lacklustre performance by Frank Lampard's side, who missed the chance to go second.
It was a well-deserved victory for Arsenal, who climb to 14th and will hope any talk of a relegation battle is now behind them.
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