Everton settled quickly into the game as Ross Barkley miscued an early effort. However, they went much closer moments later when Aiden McGeady hit the post with a curling shot after cutting in from the wing.
McGeady looked dangerous and worked space for a shot, but his attempt was poor and Brad Guzan made a simple stop.
Villa then enjoyed a rare spell of pressure and a promising move ended with Ron Vlaar trying his luck with a volley, but his effort went over the crossbar.
However, Bacuna put the visitors ahead when he slotted the ball home from Benteke's pass.