Nolan hit a second half double as the Hammers picked up a vital win.
The game had been billed as a six-pointer although West Ham were without Andy Carroll who lost his appeal to have his red card he picked up against Swansea overturned.
After struggling to break down Villa in the first half, West Ham pierced the home side's defence when Stewart Downing fizzed a low cross that Nolan turned home with a sumptuous backheel.
And after waiting 46 minutes for the opener, Nolan made it two just two minutes later when he broke into the box before finishing emphatically past Brad Guzan.
Sam Allardyce masterminded West Ham's third shutout of the season [PA]
Villa had the chance to reduce the deficit 25 minutes from time, but Marc Albrighton's rasping shot cannoned off the woodwork.
Christian Benteke then hit the bar when he was picked out by Albrighton.
But West Ham saw out the game to claim their third straight clean sheet.
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