Danny Ings scored a late equaliser as Burnley made it seven points from the last three games against Aston Villa.
Ings made it six goals in his last six starts for club and country when he cooly converted a penalty with just three minutes to go.
And the Clarets could have gone on to complete a remarkable comeback with Ings and substitute Lukas Jutkiewicz both going agonisingly close right at the death.
Earlier, Joe Cole had given the visitors a lead shortly before the break.
Michael Keane made his first start for the Clarets as he replaced injured Michael Duff in the only change to the team that won away at Stoke City last weekend.
Meanwhile, Scott Arfield, who missed the trip to Britannia Stadium with a knock, was back among the substitutes.
Aston Villa manager Paul Lambert handed a starting berth to former England international Cole.
And it was the visitors who had the better of frantically-paced opening exchanges.
Gabriel Agbonlahor combined with Cole, who began the game in the number 10 position, before seeing his well-struck effort blocked behind.
From the resulting corner, Dean Marney had to be on his toes to clear the ball off the line after it last came off Keane in a goalmouth scramble.
And it was Marney to the rescue again following one more set piece on 11 minutes. This time, a towering header by Ciaran Clark hit the Burnley midfielder on a head before going out for yet another corner.
The Clarets also threatened early on, though. Michael Kightly cleverly got away from his marker inside the box and dragged a left-foot shot just wide of the post.
Moments later, David Jones’ inviting free-kick into the danger area only just avoided George Boyd at the far post.
Chances kept on coming. Agbonlahor played a one-two with Cole only for Tom Heaton to guess the right way and deny the Villa captain one-on-one.
The Burnley goalkeeper then made a comfortable save when Tom Cleverley tried his luck from outside the penalty area.
In response, George Boyd did likewise on the half-hour mark, without seriously troubling Brad Guzan in the visitors’ goal.
Despite the match slowly settling down, Aston Villa went in front on 37 minutes.
The ball broke to Andreas Weimann on the right wing and his low ball in was sloted into the net at the near post by Cole.
The Clarets replied instantly. Ings controlled the ball wonderfully well just outside the box and produced a well-hit effort that Guzan did well to push away from danger.
Burnley kept the pressure on until the break, but had to come off the pitch for half-time trailing.
They threatened again straight after the restart, though. Ings made a good run into the channel and pulled the ball back to Boyd who saw his right-foot shot blocked in the nick of time by Alan Hutton.
Then on 55 minutes the Clarets must have thought they’d equalise.
Ings knocked the ball down right into the path of Kightly whose first-touch took him one-on-one against Guzan only for the Villa goalkeeper to spread himself and produce an outstanding save before Clark cleared the
ball away from danger.
At the other end, Villa kept threatening on the counter-attack and Heaton made another good stop as he pushed away a deflected effort from Ashley Westwood.
Jutkiewicz and Arfield were introduced into the action as Burnley kept their search for an equaliser.
And the striker went inches away from making an immediate impact.
Kieran Trippier whipped in a sensational cross from a free-kick that Jutkiewicz only just failed to connect with in front of goal.
All in all, however, the visitors seemed to control the game well as it approached the final 10 minutes.
It was Burnley who had the final say on the outcome, though.
On 87 minutes, Jutkiewicz showed great strength inside the box before being brought down by Jores Okore.
Man-of-the-moment Ings stepped up and calmly sent Guzan the wrong way to equalise from the spotkick.
And it could have got even better right into injury time.
Substitute Ross Wallace first found Ings in the penalty area and the Clarets number 10 took a good touch before striking the ball against the base of the post.
Moments later, the Scot this time lofted the ball into the danger area on his weaker foot before Jutkiewicz headed it agonisingly wide of the post with the Villa goalkeeper all but beaten.
All in all, however, Sean Dyche’s team could have still been satisfied as they came from behind to get a point for the second time this season.
Burnley: Heaton; Trippier, Keane, Shackell, Ward; Boyd, Marney, Jones (Wallace 83), Kightly (Arfield 65); Ings, Barnes (Jutkiewicz 65).
Subs not used: Gilks, Long, Mee, Sordell.
Aston Villa: Guzan; Hutton, Okore, Clark (Lowton 90+5), Cissokho; Westwood, Sánchez; Weimann (Richardson 78), Cole (Grealish 67), Cleverley; Agbonlahor.
Subs not used: Given, Bacuna, N’Zogbia, Robinson.
Goals: Ings 87 pen – Cole 39
Bookings: Kightly, Marney, Barnes – Cleverley, Hutton, Okore
Referee: Graham Scott
Attendance: 19910 (4046 away)