Ukraine forward Andriy Yarmolenko scored an emotional goal on his return to set West Ham on their way to a crucial win in the race for fourth.
After coming off the bench for his first appearance since the Russian invasion of his homeland, Yarmolenko was in tears after he fired the Hammers ahead in the second half.
Pablo Fonals added a second and West Ham survived a nervy finish after Jacob Ramsey pulled a goal back for Villa.
The win moves West Ham back to within two points of Manchester United in the battle to qualify for the Champions League.
It might have come at a cost after Michail Antonio and Aaron Cresswell were both forced off with injury in the second half at the London Stadium.
Antonio went off with what looked like another hamstring issue and both players are now a doubt for the second leg of the Europa League last-16 tie with Sevilla on Thursday.
But for now, West Ham can savour an important win against a Villa side who had won three straight games under Steven Gerrard.
West Ham started the day five points behind Manchester United in fourth place after their win over Tottenham on Saturday and the Hammers were frustrated in a scrappy first half.
The home side dominated for most of the opening 45 minutes but it was the same old story as they failed to capitalise after getting into some decision positions.
Tomas Soucek headed wide, Philippe Coutinho threatened at the other end for Villa but just three shots on targets told the story of a pretty forgettable half.
West Ham were dealt major double injury blow early in the second half when Antonio and then Cresswell were forced off.
Antonio went down holding his left hamstring in what will be a huge concern for Moyes.
Yarmolenko was given a standing ovation as he came on to replace Antonio.
Lukasz Fabianski made a great save to turn a Danny Ings header on to the post before then Dawson missed a sitter at the other end.
Villa goalkeeper Emi Martinez did well to save a powerful Kurt Zouma header from a corner before Dawson somehow headed the rebound over from about two yards out.
West Ham stepped it up and went ahead on 70 minutes when Yarmolenko controlled a pass from Said Benrahma before turning and firing a finish past Martinez.
Fornals made it two on 82 minutes when he finished off a brilliant team move after a great run from Declan Rice from deep inside his own half.
Ramsey pulled a goal back for Villa in the 90th minute but West Ham survived a nervy finish to secure a crucial win.
