Ings continued his prolific scoring for the Saints, having now netted 25 of their 54 goals since the start of last season, as he struck in the fifth minute at Turf Moor.
Injury-ravaged Burnley had an appeal for a penalty rejected when Chris Wood went down after Polish defender Jan Bednarek laid his hands on his back and there was more controversy involving the New Zealand international after the break.
Wood got behind the Saints defence to latch on to a long ball but the assistant flagged for offside with the Burnley striker continuing his run and putting the ball in the net.
VAR rules instruct officials not to flag or whistle until a move is complete, leading to confusion and frustration on the bench with the Burnley staff believing Wood was onside.
England international Ings had the ball in the net again in the final minutes but that too was disallowed for offside.
Both teams had lost their opening match.