Ings notched his first of the afternoon on 12 minutes, tapping in after Begovic spilled Ashley Barnes’ cross-come shot and doubled his tally just 90 seconds later, when he latched onto Michael Kightly’s curled centre to silence a stunned Britannia Stadium.
Jonathan Walters’ diving header reduced the deficit in the 32nd for Stoke but Burnley’s valiant defensive performance was rewarded with a second successive win that sees them leapfrog Queens Park Rangers and, provisionally, Crystal Palace in the standings.
Burnley boss Sean Dyche had stressed after the Hull win the importance of building on that result, and it certainly seemed those words had been absorbed by his players in the opening stages here as the visitors raced into a two-goal lead.
On an individual level, those strikes also marked a continuation of momentum for Ings, who had netted twice for England Under-21s at his home ground Turf Moor during the international break.
But as Ings grabbed his second and third league goals this term, it was apparent that Stoke – without injured duo Marc Wilson and Erik Pieters in defence – had provided him with a helping hand for each goal.
First, Pieters’ replacement Marc Muniesa lost the ball and in the move that followed, Asmir Begovic’s parry from Ashley Barnes’ cross teed Ings up nicely for a slotted finish.
Then, just over a minute and a half later, Burnley’s former Stoke man Michael Kightly got the better of Phil Bardsley and had the space to burst forward down the left and cross to an unmarked Ings, who once again made no mistake.
Stoke then began to get into the game, with the lively Bojan Krkic having a shot deflect wide. Soon after, the Spaniard provided the delivery which Walters converted with a diving header, goalkeeper Tom Heaton getting a hand to the effort but unable to keep it out.
Victor Moses then had penalty claims waved away after going down in the box in a tumble, before curling in a shot that Heaton palmed away.
Stoke’s quest for an equaliser continued after the break as Moses steered wide. He then departed the field clutching his thigh, with Marko Arnautovic coming on in his place.
The Clarets held firm with some brave defending and might have even scored a third goal during the closing stages as Begovic denied substitute Lukas Jutkiewicz.
The Burnley goal was still not out of danger, with Begovic joining the action at that end and passing up the last real opportunity of note, heading off-target from a corner.