Benteke doubled the Villans' advantage in the 11th minute, tapping in a Weimann cross.
Karim El Ahmadi set up the Belgian's second, feeding the ball through just before the half-hour mark for the striker to power it in.
Benteke completed his hat-trick six minutes later, slotting a low effort into the Crewe goal and leaving Phillips rooted to the spot in the process.
The League One side were able to reduce the deficit before half time as Harry Davis smashed the ball in from close range.
Bacuna's extended stay on the pitch paid off seven minutes from full time when he picked the ball up on the edge of the penalty area, took it past two defenders and drove it into the top corner.
The result gives Villa their first pre-season victory.