Palace nearly made the perfect start when Wilfried Zaha was played clean through, catching Tyrone Mings on his heels, but Villa goalkeeper Emi Martinez was equal to the attempt.
The hosts then took the lead only five minutes in, when Bertrand Traore played in Ollie Watkins down the right and was on hand to thump the ball into the net after Vicente Guaita parried Watkins’ shot into the middle of the box.
Villa were then, however, reduced to 10-men when Mings stuck out an arm to block Zaha and was shown a second yellow on the stroke of half time.
Despite their numerical disadvantage, Villa continued to enjoy the better of the game in the second half.
And the second goal that arrived in the 66th minute was no more than they deserved. Palace failed to defend an El Ghazi free-kick, Watkins headed against the crossbar and Hause followed up to score his second Premier League goal for Villa.
With Palace forced to commit more men forward, Villa looked even more dangerous, and, after Watkins saw a shot blocked, he teed-up El Ghazi for his fourth goal in four games.
The result lifted Villa into the Premier League’s top six – for a few hours at least – while Palace have now conceded 10 goals in two matches after last weekend’s hammering by Liverpool.