The striker's header ensured that Sean Dyche's team ended the season - which saw them suffer the pain of relegation - with a victory over Tim Sherwood's men on Sunday
Ings is set to leave Turf Moor in the summer following Burnley's return to the Championship at the end of his contract, but his headed goal at Villa Park will add to the demand for his services from top-flight clubs as he took his tally for the campaign to 11.
The goal was enough to settle a scrappy contest on the final day of the season and send Villa to Wembley to face Arsenal in the FA Cup final next weekend on the back of two consecutive defeats.
Tim Sherwood's side slumped to their 20th league defeat of a miserable season, in which they amassed just 38 points but managed to cling on to Premier League survival.
Sherwood drafted young goalkeeper Jed Steer into his starting line-up, resting Shay Given after Villa's 6-1 drubbing at Southampton, while Burnley handed a first start to Freddie Ulvestad.
Villa were slow to get going and their lack of urgency was punished after six minutes, when Kieran Trippier's cross was met by a poor defensive header from Leandro Bacuna.
The ball was knocked straight back into the box, where Ashley Barnes rose above Bacuna and teed up Ings for a looping header that Steer could not prevent from dipping into the net.
Ron Vlaar should have had Villa level when he connected with Gabriel Agbonlahor's knock down and hit a fierce shot that flashed just over the crossbar.
Misplaced passes and disjointed play made for a scrappy contest, but Burnley provided occasional moments of quality and George Boyd's tricky run down the right produced a cross to Ings, who lashed a volley over from close range.
Christian Benteke spurned two chances to draw level, firing wide from a Bacuna cross before seeing his diving header saved by Burnley goalkeeper Tom Heaton.
Villa were energised by the interval and charged forward in the second half, with Benteke and Fabian Delph probing for an opening in a resolute Burnley rearguard.
Benteke gifted Agbonlahor with a golden opportunity to equalise, finding him in acres of space on the edge of the box, but he fired a disappointing low shot that was saved by the feet of Heaton.
Heaton showed the kind of form that earned him an England call-up this week with a brilliant diving save to keep out Charles N'Zogbia's stinging drive from 20 yards.
In the end, Burnley had their goalkeeper and their top scorer to thank for their winning end to life in the Premier League, and they may find it difficult to hang on to both Ings and Heaton as they rebuild for next season in the Championship.
IN PICTURES The final day of the 2014-15 Premier League season