The Hammers travelled to Arsenal on Wednesday night and won 2-0 to send them to sixth in the Premier League table.
Goals from Tomas Soucek and Konstantinos Mavropanos helped seal their fourth league win against the 'big six' sides this season.
Doubts over Moyes' position as boss were raised earlier in the campaign when West Ham went on a run of one win in six matches.
However, the east London side have proved their quality against the big sides and O'Hara believes Moyes deserves to be rewarded for it.
Speaking on talkSPORT Breakfast the morning after their huge win away at Arsenal, he said: "West Ham, fair play.
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"I mean, David Moyes comes in for a lot of criticism about a pragmatic style of football, but this man can go away from home and get a result at top of the table, it's a huge, huge result.
"We had Ray Winstone coming on and moaning about the Carabao Cup [5-2 defeat to Liverpool], they are flying in the Premier League. They're sixth in the table, their form is absolutely sensational.
"In my opinion, David Moyes deserves a new contract, what are you waiting for? I don't know what people are looking for out of West Ham, you're never going to be Arsenal, you're never going to be Liverpool, you're never going to be Man United.
"You are punching above your weight, sixth in the table is the peak, is the top of where West Ham can be. David Moyes, give him a new contract and let him go and do his thing.
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"He's signed good players this season and he deserves a new deal. Why do you have to get rid of him, why do they have to make a change, why?"
Moyes initially joined West Ham in late 2017 and guided them to Premier League safety before leaving at the end of the season.
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He returned in 2019 and has been at the helm ever since, with the Scotsman leading them to Europa Conference League glory in June.
West Ham are four points off the Premier League top four and through to the last 16 of the Europa League as Moyes and co. enter 2024 on a high.