In the early stages of the game Nathan Baker inexplicably played Dave Martin through with a poor back pass, but the Luton striker blasted the ball into the side-netting when one-on-one with Jed Steer.
The Conference side took the lead on the halfway mark through John Shaw. Shaun Waley played the ball to Mick Cullen, whose cross from the right flank found Shaw, who then fired into a gaping net.
Benteke was replaced by 18-year-old Callum Robinson at the break, as the away side searched for an equaliser.
Villa, who made 10 changes on the hour mark, searched in vain for an equaliser as the non-league side held firm to secure an impressive victory.