The Clarets were thankful to Ings’ fourth goal in five Premier League matches late in the game after Joe Cole handed Villa the lead.
Villa looked to be on course for their first win in nine games when Cole grabbed his first top flight goal on the season on his first start for the club in the first half.
The former England International slotted home Andreas Weimann’s sliderule pass seven minutes before the break.
But Jores Okore dragged down Lukas Jutkiewicz in the area for a penalty late on in the game and Ings made no mistake from the spot for the equaliser.
Burnley were looking to make it three wins in a row in the top flight for the first time in almost 40 years and Ings could have scored his fifth goal in five games but hit the post in stoppage-time.
Cole was at the heart of things straight away, linking up well with Gabriel Agbonlahor, Andreas Weimann and Tom Cleverley.
Villa almost went ahead inside five minutes, with Agbonlahor’s deflected shot earning a corner from which Dean Marney headed smartly off the line after Jores Okore’s poked effort had spun towards the top corner off Keane.
Burnley looked particularly vulnerable from Ashley Westwood’s corners, and Marney was on hand again shortly afterwards with a vital block when Ciaran Clark got his head to another inswinger.
The Clarets struggled to clear their lines but, when they did, they looked dangerous on the break and Carlos Sanchez had to be alert to stop Ings running through on goal from his own half.
Michael Kightly also threatened after a smart turn in the area fooled Villa but his shot just missed the far post.
Agbonlahor was finding lots of space and should have done better in the 19th minute when he was cleverly played in by Cole but shot tamely at Tom Heaton.
The former England man was at the heart of everything and it was fitting he should be the man to open the scoring.
A misplaced Burnley header played in Weimann down the right and his smart pass was turned in at the near post by Cole, who was definitely onside despite the protests of the home side.
Ings was Burnley’s brightest spark and he tested Brad Guzan with a fierce shot after a fine piece of control on the edge of the area.
Ashley Barnes came even closer in injury time with a header against the far post but referee Graham Scott, taking charge of his first Premier League game, errantly ruled the ball had come off his hand and then showed Barnes a yellow card for his protests.
Burnley continued to push for an equaliser early in the second half, with George Boyd seeing a tame shot blocked and then Kightly doing superbly to break through the Villa defence only for Guzan to pull off an excellent save, with the ball cleared from in front of the line.
The game remained open, and it was Heaton showing good reactions in the 57th minute to block an effort from Weimann.
Burnley boss Sean Dyche made a double substitution with 25 minutes to go, sending on Lukas Jutkiewicz and Scott Arfield for Barnes and Kightly.
Jutkiewicz almost made an instant impact but Kieran Trippier’s dangerous free-kick just evaded the big striker in front of goal.
Cole’s afternoon also came to an early end, Jack Grealish the man replacing him, but the midfielder had certainly more than justified his place in the side.
The game looked to be petering out until a ball over the top caught out Okore, who clumsily brought down Jutkiewicz in the box.
The Villa defender was fortunate only to be shown a yellow card but Ings exacted the main punishment by lashing the penalty high into the net in the 87th-minute.
Burnley had the better of a frantic finish, with Ings and Jutkiewicz both missing great chances, while Villa will also feel they could have won it after Grealish shot straight at Heaton.
Burnley: Heaton (6) Trippier (7) Keane (6) Shackell (6) Ward (6) Boyd (6) Jones (7) Marney (6) Kightly (6) Ings (8) Barnes (7)
Used subs: Arfield (5) Jutkiewicz (6) Wallace (5)
Aston Villa: Guzan (6) Hutton (6) Okore (6) Clark (7) Cissokho (6) Westwood (6) Sanchez (5) Cleverley (5) Cole (8) Weimann (7) Agbonlahor (7)
Used subs: Grealish (7) Richardson (5)
Man of the Match: Danny Ings