Crewe had 17 shots in the game but were ultimately outclassed by their Premier League opponents.
Speaking after the game, Villa boss Dean Smith said: "It wasn't as safe as the scoreline suggested -Crewe made a game if it.
"But I thought we were very, very clinical and our quality showed, particularly with our second goal. After that we were very good and ran away with it.
"Only Jota kept his place so there were a lot of players who haven't played since pre-season, but everyone knew their jobs, roles and responsibilities. Their application was first-class and they deserved that result."