Tokelo Rantie looked to have secured a dream result for Eddie Howe - who walked out on the Clarets last November to return to Bournemouth - with a superb 25-yard strike four minutes into the second half.
But in-form Ings, a former Bournemouth striker whom Howe signed during his spell as Burnley boss, had the last say by heading home from close range in the 84th minute.
The result leaves the Clarets still a point clear at the top of the league with Leicester losing at home to Nottingham Forest and QPR only able to snatch a 1-1 draw at Reading.
It was a high-tempo start at Turf Moor with both sides setting their stalls out in the early exchanges, Brett Pitman going close for the visitors in the third minute with a deflected drive that Burnley goalkeeper Tom Heaton did well to tip over.
Sam Vokes then went close for the home side, heading over a David Jones free-kick at the far post.
Burnley captain Jason Shackell saw his header hooked off the line by Pitman in the 23rd minute as Sean Dyche's team looked to press home their advantage.
Visiting keeper Lee Camp did well to parry Dean Marney's stinging drive 10 minutes later but Vokes really should have done better with the rebound.
Despite being under pressure for much of the first half, it was Eddie Howe's side who drew first blood four minutes after the restart.
The lively Rantie turned his man 25 yards from goal before unleashing a drive that cannoned in off the crossbar leaving Heaton with no chance.
Dyche shuffled his pack on the hour mark by introducing Keith Treacy and it almost brought about an immediate impact but the Irishman could only direct his header at Camp.
The Bournemouth keeper breathed a sigh of relief five minutes later when Vokes' shot almost slipped in at the near post after the Welsh international sprang the offside trap before going wide.
Referee Michael Russell then infuriated the home fans by turning down penalty shouts after Elliott Ward appeared to shove Ings as the striker looked to steady himself on the edge of the box.
The Clarets continued to push but it was quickly turning into a disappointing day at the office for the Championship leaders until Ings headed home six minutes from time.
Substitute Junior Stanislas lofted in a measured ball which Vokes flicked on for his strike partner to nod past a hesitant Camp.
Treacy almost hit what would have been the winner two minutes later but his free-kick from the edge of the box was clawed away by Camp.