United's Marcus Rashford wins the ball off a Palacian but then slams his long-range shot over the bar.
Romain Perraud tries to get past Bryan Mbuemo down the left but the Brentford winger is too strong for him.
Villa go back ahead and it is an own goal on debut from the unfortunate Harry Souttar.
Lucas Digne's low ball into the box from the left finds Ollie Watkins, who turns and fires a low ball across that takes a big hit off Souttar's leg and finds the net.
Villa had been threatening it after having their early momentum checked by that Leicester leveller.