Villa have managed just 11 goals in 20 Premier League matches this season, scoring only one in their last five, and looked set for a replay at Bloomfield Road after struggling to break down one of the most porous defences in the Championship.
However, Benteke rifled home from the edge of the penalty area late on to give the home side an unconvincing win at Villa Park.
The hosts failed to get a single shot on target in the first half, as Blackpool looked more than capable of causing an upset.
Paul Lambert's side upped their game after the interval, though, and Benteke's winner ended the hopes of the Championship's basement club.
Villa midfielder Ashley Westwood made a welcome return from a knee injury for the hosts, having spent a month on the sidelines, while Blackpool made three changes from their 1-1 league draw with Rotherham United last weekend.
The hosts made the early running, but Jack Grealish failed to find a Villa shirt after capping a slick passing move with a dangerous cross into the area, before Jores Okore fired over from a corner.
Alan Hutton saw his protestations ignored when he was brought down by Charles Dunne on the edge of the Blackpool penalty area, and the full-back saw yellow when he hit Dunne with a return challenge soon after.
Blackpool finally started to threaten the Villa goal shortly before the half-hour mark, and Spanish midfielder Andrea Orlandi drilled wide from a well-worked corner routine.
The former Swansea City man again caused problems for the home defence moments later – goalkeeper Shay Given getting down well to keep out his deflected strike.
Villa had two chances to break the deadlock before the end of the half, but Hutton's effort deflected harmlessly into the arms of Joe Lewis, before Benteke hit the side-netting from a tight angle.
Former Villa man Nathan Delfouneso placed the ball wide from a promising position 10 minutes into the second half, only to see the linesman had already raised his flag for offside.
It took Villa until the 58th minute to get a shot on target – Benteke having a soft header saved by Lewis before Carlos Sanchez also tested the goalkeeper.
Lewis had to be alert again moments later when he pushed a Benteke half-volley onto his left-hand post, with Villa beginning to dominate proceedings.
However, with home fans chanting 'We only want one goal', Benteke duly obliged, thrashing the ball in after cutting in from the left, somewhat banishing memories of last season's third-round embarrassment at the hands of Sheffield United in the same round.
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