Jack Grealish put the visitors ahead after just four minutes thanks to John McGinn's assist.
McGinn was again provider for Villa's second as Conor Hourihane steered the ball past Alphonse Areola.
Tyrone Mings wrapped the game up early in the second half to stab home Hourihane's free-kick.
Speaking after the game, Villa manager Dean Smith said: "It was a good all-round performance, we've got the balance just right at the moment.
"We've got some good quality going forward and there's a real desire to keep the ball out of the back of the net at the moment which is really pleasing.
"It's the balance between defence and attack. It's something that's very hard to get right in football.
"Before lockdown we were guilty of being gung-ho trying to win games. After lockdown, we defended deeper and in numbers. We scored some good goals tonight and we showed resilience to keep a clean sheet."