Defender Gabriel Magalhaes scored the only goal of the game in the 64th minute with a header from Bukayo Saka's corner.
The win saw Arsenal maintain their unbeaten start to the Premier League season and they are two points behind leaders City going into the eagerly-anticipated clash at Etihad Stadium.
Neville believes that Arteta will largely persist with the team that produced an excellent defensive display against Tottenham.
Gary Neville has named the one change that he thinks Mikel Arteta should make to his team for the clash against Manchester City
Neville believes that the only alteration against City will see Rice return from suspension at the expense of Jorginho.
Leandro Trossard was deployed as an attacking midfielder against Tottenham in the absence of captain Odegaard, who is out with an ankle injury suffered while playing for Norway.
Neville believes that Trossard performed well and will retain his place in the starting lineup.
Speaking on the Gary Neville Podcast, Neville said: 'I think he [Rice] will come in just for Jorginho and then leave it as it is.
'I think Trossard did well in that role – the number 10 – so I don't think he'll change that.
'I think he'll keep it simple. I don't think Mikel Arteta is doing anything nowadays that is surprising us and I say that in a positive sense and a complimentary sense.
'He's got such confidence in his own team and how they play he doesn't need to try and think of fancy different systems or shocking anybody with the team selection. He's got stability.
'When you've got stability and an 11 that works together well and you can just change one or two then there is no need to do anything clever.'
Before facing City, Arsenal will commence their Champions League campaign on Thursday with an away game against Atalanta.
Neville believes that Arteta won't rotate too heavily for that fixture beyond bringing in the likes of Raheem Sterling and Gabriel Jesus, who featured as substitutes against Tottenham.
He said: 'You can trust the 12 or 13 players that are his best players. He might bring in [Gabriel] Jesus and [Raheem] Sterling on Thursday night but I don't think he will be doing mass rotation.
'You can't afford to do that and I don't think you should do that. You have to trust that these players are capable physically of handling a Sunday-Thursday-Sunday [schedule].'
As well as Odegaard, Arsenal are without defenders Riccardo Calafiori, Takehiro Tomiyasu, Oleksandr Zinchenko and Kieran Tierney due to injury, with midfielder Mikel Merino also sidelined.