The England Under-21 striker netted twice in as many minutes in the opening quarter of an hour as Sean Dyche's side made a flying start at the Britannia Stadium.
Those goals sparked Stoke into action, as the hosts poured forward for the remainder of the game, managing to pull one back through Jonathan Walters shortly after the half-hour mark.
Stoke remained in the ascendancy after the interval, but despite dominating play, Mark Hughes' team were unable to find an equaliser as the Burnley backline stood firm.
The Staffordshire side's cause was not helped by losing Victor Moses 10 minutes into the second period, the Nigeria international limping out of the action after proving a constant threat down Stoke's left-hand side.
For Hughes' men, who had defeated Tottenham 2-1 before the international break, it was a disappointing return to action against a Burnley side who came into the match bottom of the table.
Thanks to their first away win of the season, Dyche's outfit climbed up to 18th, with only goal difference separating them from a spot outside the bottom three.
The home side were forced into two changes from the game at Tottenham, as Geoff Cameron and Marc Muniesa replaced the injured duo of Erik Pieters and Marc Wilson in defence.
Burnley's only alteration saw former Stoke man Michael Kightly come in for Scott Arfield, who picked up a knock in training.
Ings opened the scoring with the first action of note in the 12th minute, converting a simple rebound after Asmir Begovic parried Ashley Barnes' low cross into his path under pressure from Kightly.
A minute later Ings doubled his and Burnley's tally as Kightly got free down the left and delivered a pinpoint delivery for the striker to tap home from six yards.
Following the double salvo, Stoke pinned the visitors back inside their own half and halved the deficit in the 32nd minute when Walters' header from Bojan Krkic's excellent cross was too strong for Tom Heaton to keep out.
The Burnley goalkeeper was called into action again just before half-time as he leapt to his left to palm away a curling effort from Moses.
Marko Arnautovic, brought on as a replacement for Moses, dragged a low shot wide from the edge of the box soon afterwards.
Peter Crouch was also introduced from the bench and his flicked header was just out of reach of a stretching Steve Sidwell at the far post.
Despite enjoying the majority of possession and bombarding the Burnley penalty area, Stoke could not find a way through as the visitors manfully held on to claim maximum points.
