With QPR not playing until Monday the Clarets knew a win against the Lions would see them go straight back into the automatic promotion places.
However the lead lasted just two minutes before Ings equalised, and Burnley went in at the interval ahead as Dean Marney struck just before half-time.
And Ings made sure of the result with his 24th of the season just after the hour mark as Burnley maintained their proud record of being the only team in the Championship yet to lose at home this season.
Despite heading to Turf Moor having won just one of their last 10 games, Millwall started the brighter and after Lee Martin had fired wide Woolford gave the Lions a deserved lead as he superbly volleyed past goalkeeper Tom Heaton to open the scoring.
But the Lions have the worst goal difference in the league and just two minutes later Burnley were level as Ings turned in the box and curled past the helpless Stephen Bywater.
Ings should have put the home side ahead in the 44th minute after he was brought down in the penalty area by Nadjim Abdou, but his spot-kick was saved low down to the right by Bywater.
However Burnley did go into half-time in front as just moments later Marney let fly from 25 yards.
Both teams looked cagey in the opening stages of the second half but it was the hosts who had the first opening.
Excellent work from Kieran Trippier allowed Sam Vokes to shoot from a tight angle but Bywater saved well low down.
Just after the hour mark the hosts increased their lead as Ings brilliantly controlled Trippier's long ball forward before finishing past Bywater with his second touch.
Millwall began to come into the game and almost made it 3-2 after Ryan Fredericks' cross-cum-shot clipped the bar, to the relief of Heaton.
Burnley's Ashley Barnes almost made an instant impact after coming on in the 75th minute but his goalbound strike was well blocked.
Ian Holloway's visitors pushed for a second but struggled to create a clear-cut opening despite possession in the final third.
As the game approached the final 10 minutes, Kightly picked the ball up on the right before dribbling inside across the face of the box and shooting - but Bywater saved easily.
Moments later Bywater again denied Kightly and Ings came close to hat-trick as his header from the resulting corner edged narrowly wide.
With the last chance of the game Junior Stanislas' free-kick was tipped over by Bywater as Burnley ran out comfortable winners in the end.
- Sports & Recreation
- Martyn Woolford
- Dean Marney