A late goal from substitute Emile Heskey rescued a point for Martin O'Neill's side at a wet and windy Turf Moor.
Burnley were unchanged from the side which earned their first away point of the season a fortnight ago at Eastlands, while Villa made just one change from the side that thrashed Bolton with Stiliyan Petrov replacing Nigel Reo-Coker.
Burnley went in front after Robbie Blake had been fouled by Steve Sidwell. From the resulting free-kick taken by Blake himself, the Clarets skipper beat Brad Friedel to the ball for his first Premier League goal.
Cameroon international Andre Bikey had two attempts to increase Burnley's lead, firstly shooting over from the edge of the penalty area and then heading a Blake corner wide of the target.
Villa's best chance in the opening half came after hesitation from Burnley goalkeeper Brian Jensen which was seized upon by Gabriel Agbonlahor who found Ashley Young who was unfortunate to see his attempt drop the wrong side of the crossbar.
With the elements in their favour in the second half Villa enjoyed plenty of possession and Agbonlahor was denied by Jensen at the expense of a corner when clean through.
The home team had to rely on the counter-attack with striker Steven Fletcher producing a fine left-foot shot which Friedel did well to turn over the crossbar.
Both managers rang the changes with Villa introducing Stewart Downing after the wide-man's recovery from a long-term injury following his transfer from Middlesbrough.
But it was another substitute, Heskey, who ensured that Martin O'Neill's side left Turf Moor with a point when the substitute headed home from close range following a cross by James Milner.
While the result will no doubt disappoint Burnley manager Owen Coyle after his side were in front for most of the game, his team nevertheless demonstrated once again that this corner of East Lancashire will be a difficult place for opponents to come and collect points.
The result also ensures that while these two sides may not have met for many years, Burnley had not lost against Villa in 23 games.
After scoring so close to the end of the game Villa will no doubt be happy enough with the point but their away form remains a matter of concern when compared to the fine performances on the road which Villa turned in last season.