Ex-Burnley midfielder Martin Paterson scored twice for the Terriers on his first return to Turf Moor since leaving in the summer, but it was not enough for the visitors.
The Clarets got off to the best possible start when Ings put the hosts in front after just five minutes.
The hosts, the only side still unbeaten at home in the Championship, would have doubled their lead had Sam Vokes not rushed his 15th-minute shot which flew harmlessly wide.
But Huddersfield drew level when Paterson turned home an Oliver Norwood corner to level the scores on 20 minutes.
Right on the half-hour mark, Jones found space on the edge of the area to turn and wrap his reliable left boot around a shot which Smithies was able to acrobatically keep out.
Minutes later, Ings was through on goal when he was brought down by Murray Wallace, who was lucky to only see yellow.
The resulting free-kick from Jones cannoned back off the crossbar before being cleared to safety by a grateful Terriers defence.
It seemed inevitable that Burnley's mounting pressure would eventually count for something and it did with Ings' second goal of the game just before half-time to restore the hosts' lead.
Right-back Trippier teed up the former Bournemouth forward, whose shot with the outside of his right foot left Smithies with no chance.
Sean Dyche's men began the second half where they left off, a quick 54th-minute breakaway had Huddersfield outnumbered at the back, but Vokes wasted his chance to increase the deficit.
More good counter-attacking football led to a string of chances for the Clarets - Dean Marney's sliding shot did no justice to the fine build-up work by the resilient Vokes.
The Welsh international decided to go it alone shortly after and found himself one-on-one with Smithies, but could only blast over from 15 yards.
However, a flying run from Trippier ultimately secured the victory for the hosts. He calmly rounded Smithies before firing a shot that went in off the underside of the bar.
There was still time for Paterson to create a nervy end when he latched onto a superb low cross from Paul Dixon with a minute remaining, but Burnley held on for just their third win in 11 Championship matches.
- Sports & Recreation
- Alex Smithies
- Martin Paterson
- Kieran Trippier
- Sam Vokes