Lowly Southampton threatened to pull off an almighty upset as Cameron Archer beat David Raya to silence the Emirates crowd in the 55th minute.
But the home team hit back with an immediate equaliser through Kai Havertz, before goals from Gabriel Martinelli and Bukayo Saka put the contest to bed.
The result leaves Arsenal in third place, with Liverpool holding a one-point lead over the Gunners and champions Manchester City at the top of the Premier League table.
At the same stage last season, City sat in Liverpool's position - with a one-point advantage at the summit - and Pep Guardiola's side will look to reclaim top spot when they travel to Wolves after the international break.
'I said before the game about Arsenal and City getting the job done today and they've got their jobs done,' former Manchester United and England right-back Neville said on NBC Sports after City survived a scare to defeat Fulham.
'But I think for City, other clubs will look at that and see that Fulham have scored twice.
'Then on Arsenal, Russell Martin, Southampton's manager, called them soft, lacking in fight and spirit... I think he'll have probably changed his mind after today because they did put up a real show for large parts of that game.
'But Arsenal got there in the end and I think it's an important one for them going into the international break.'
'It's mind-blowing to me. I think when [Jose] Mourinho came [to Chelsea] in the mid-2000s, he changed the game,' he added.
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'Mourinho came in and then went so far in front, starting really quickly out of the blocks, and it got to the point whereby you can't afford to go behind in terms of points before Christmas.
'I think that's the same now with Pep Guardiola. If you think about Jurgen Klopp's Liverpool and now Mikel Arteta's Arsenal, having to chase them all the time.
'You have to stay with them right from the very beginning.'
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