Benteke, who recently signed a new contract at Villa Park following intense speculation surrounding his future, scored all his goals in the first half as Paul Lambert's men brushed aside the League One club with little difficulty.
Andreas Weimann and new signing Leandro Bacuna also get their names on the scoresheet for Villa, with Harry Davis netting a consolation for Crewe.
Benteke, Gabriel Agbonlahor and Ron Vlaar were included in a strong starting line-up for the visitors at the Alexandra Stadium.
It took Villa just two minutes to open the scoring, Weimann firing a 25-yard effort into the top corner.
The Austrian was heavily involved in Villa's second nine minutes later, crossing from the right to set-up Benteke to double the lead.
Belgium international Benteke was in typically clinical form and hammered home his second around the half-hour mark before cutting in from the left to secure his treble in just 34 minutes.
Davis pulled one back with a close-range finish four minutes before the break.
Villa made 10 changes as the game moved into the final third, with close-season recruits Bacuna and Nicklas Helenius thrown into the fray.
Crewe's resolve stiffened as the game meandered towards its conclusion, but there was still time for Bacuna to add gloss to the scoreline, the Dutchman rounding things off with a fierce drive seven minutes from time.