Stand-in skipper Alexandre Lacazette opened the scoring for the Gunners in the 21st minute, finishing off a superb 16-pass team move.
And Martin Odegaard doubled the lead six minutes later heading home from close range.
Arsenal dominated throughout and added a third after 62 minutes with defender Gabriel nodding in a Gabriel Martinelli corner.
The Gunners jump up to fifth in the Premier League table, one point off the top four, while Southampton stay 16th.
No Aubameyang? No problem
All the pre-match talk was around Aubameyang, with Arsenal manager Mikel Arteta saying the striker was missing out “due to a disciplinary breach”.
“I think we have been very consistent, that we have certain non-negotiables in the team that we have set ourselves as a club,” Arteta added.
It is not the first time the Spaniard has dropped Aubameyang for disciplinary reasons. In March, the Gabon international missed a win over rivals Tottenham for a “breach of pre-match protocol”.
But after a slow start, pre-match incidents were soon forgotten as Lacazette converted Bukayo Saka’s cross, completing a team move that started with keeper Aaron Ramsdale.
And minutes later Arsenal grabbed a second with Odegaard meeting Alex Tierney’s header to score a third goal in as many matches.
Arsenal’s dominance continued after the break with Gabriel scoring moments after he had had a goal chalked off for offside.
Martinelli then curled a strike against the post midway through the second half, with Saka also striking the woodwork and Takehiro Tomiyasu forcing a fine stop from keeper Willy Caballero.
The hosts continued to impress in the closing stages, winning in style to end a run of back-to-back defeats.