The Lancashire club started the brighter but neither side were able to register a shot on target in the opening 10 minutes.
Sam Vokes produced a neat turn on the edge of the Addicks' box to create a goalscoring chance but dragged his shot wide.
Vokes almost broke the deadlock just after the half-hour mark when he latched onto Kieran Tripper's cross but headed narrowly past the post.
The hosts finally took the lead when Tripper produced another precise ball into the box and Ings flicked it past keeper Ben Hamer to bag his 10th goal of the season.
Burnley started the game in fourth place in the Championship, three points behind leaders Queens Park Rangers.