Nolan scored twice in as many minutes straight after the half-time interval at Villa Park as Sam Allardyce's side made it seven points from their last three games to boost their survival chances.
Villa, meanwhile, have won just one of their last eight home matches in all competitions and were twice denied by the frame of the goal as Marc Albrighton and Christian Benteke struck the woodwork.
West Ham had only scored two goals in their previous six visits to Villa heading into Saturday's game and their chances of improving that statistic appeared diminished by the absence of the banned Andy Carroll, but Nolan filled the void as talisman.
The 31-year-old midfielder has now scored seven goals against Villa – more than he has against any other Premier League side – and has netted four times in his last two appearances.
Gabby Agbonlahor returned to Paul Lambert's Villa XI following injury, while Allardyce replaced suspended striker Carroll with Carlton Cole, who spent the 2004-05 season on loan at Villa.
It was another former Villa player who had the first half's best chance. Matt Jarvis sprung the hosts' offside trap and slid the ball across goal for Stewart Downing, who somehow failed to connect with the ball when he would have had a tap-in.
Downing's composure deserted him again when well placed and Jarvis fired the ball into the side-netting from close range.
Villa offered very little in the first 40 minutes, with Benteke's touch letting him down when he was through on goal, but Ashley Westwood's fine volley went narrowly wide just before the break.
West Ham took the lead within 18 seconds of the restart. Downing tricked his way past Ryan Bertrand down the right and crossed for Nolan, whose cheeky flick took a deflection and looped over goalkeeper Brad Guzan.
Nolan made it 2-0 on 48 minutes. The midfielder did superbly to rob Fabian Delph of possession on the edge of the West Ham box before carrying the ball into the area and slotting past Guzan.
Albrighton was quickly sent on by Lambert and the winger smashed the post with a vicious 66th-minute strike. The rebound struck Adrian and went out for a corner, which came to nothing.
Substitute Albrighton then crossed for Benteke, whose first-time attempt hit the crossbar.
West Ham were camped inside their final third for the remainder of the game and had to defend a series of corners, but held on for a morale-boosting victory.
