Two second-half strikes, the first a stunning individual effort from Carles Gil on 51 minutes before Andres Weimann double the lead 20 minutes later, proved too much for the Sky Bet Championship side who dominated possession but had to settle for Callum Wilson’s consolation in injury time.
Paul Lambert’s side had only managed to score on one occasion in the six preceding games but January signing Gil ended the wait in emphatic style, cutting in from the right before finding the top left-hand corner with a curled effort from 25 yards.
The hosts doubled their lead when Weimann rounded off a fine counter with a first-time finish which evaded the reach of Lee Camp following Alan Hutton’s cross from the right.
Eddie Howe changed things as he looked for a route back into the game, and substitute Wilson struck late on to give the visitors hope of forcing a replay.
But Villa were resolute in defence and had a chance to seal the win the closing stages but ultimately held on to book their place in Monday evening’s draw.
Despite making eight changes prior to the game, the Championship leaders took just four minutes to register their first attempt, with Shaun MacDonald seeing a speculative effort from 25 yards deflected over the bar.
Shay Given, who started his first game since Villa’s League Cup exit to Leyton Orient in August, was tested moments later as Harry Arter’s effort forced him into a comfortable save.
The end-to-end nature of the of the opening exchanges presented Villa with their first chance as, moments after Arter’s effort, Hutton broke down the right wing and presented Weimann with a great chance to break the deadlock. The Austrian, however, saw his header go a foot wide of the target.
It was to be Bournemouth, though, who created the best opening of the half as MacDonald collected Arter’s flick-on, evaded the Villa offside trap – according to the officials – and rounded Given but saw his effort cleared off the line by Kieran Richardson.
Eunan O’Kane sparked a flurry of activity around the Villa area in the closing stages of the first half but again Given was up to the task, tipping his compatriot’s effort out for a corner.
The second half began in the same fashion but it was Villa who took control of the game to begin with. Christian Benteke capitalised on a defensive mistake from Bournemouth and, after dancing round three challenges found Gil in the box.
The Spaniard dropped his shoulder before firing into the side netting, but this was just a precursor for the moment of the game as he ended Villa’s long overdue wait for a goal.
Having collected the ball on the right wing, the £3.2m signing from Valencia skipped inside one defender and, in the next step, found the far left-hand corner for his first strike since joining the club.
Bournemouth continued to put Villa under pressure but failed to create a clear sight of goal, and were punished when Hutton picked Weimann in the box and, unlike his first-half header, the Austrian made no mistake in finding the back of the net.
Wilson snatched a late goal for the visitors but they ran out of time as Villa held out for a much-needed morale-boosting victory in front of their own fans.