Ings, who had earlier missed when clean through, pounced on the loose ball after Ross Wallace had kept the ball alive to stroke home his 25th goal of a prolific season.
Jordan Rhodes had put the home side ahead after 24 minutes with a clinical finish but two goals in six second-half minutes turned the game on its head.
Jason Shackell's towering header brought the scores level before Ings pounced 11 minutes from time to leave the Clarets eight points clear in second place, and Dyche praised his star striker.
He said: "I thought that Ingsy was exceptional with his work ethic. Just kept going and going and going, and the demand he's got on himself and the rest of the group is first class because some strikers, if it's not quite landing for you, just switch off.
"He doesn't. He just keeps going and I think he got his rewards. He's a fantastic person as well as a player."
It ended a run of 11 meetings since Burnley defeated their fiercest rivals and Dyche could not hide his satisfaction for the fans who have had to wait so long for this victory.
"I'm delighted for the fans because it's 35 years," Dyche said.
"People like me, you'll see a number of people come and go out of this game, and it's about that here, about the supporters having something to believe in. So I'm really pleased for that, and for the board as well, they're all Burnley fans."
The result continues Burnley's march to promotion. They have lost just three league games all season - none in this calendar year - and they stretched their unbeaten run to 12 games.
And Dyche was left in no doubt that the goal would come because of his team's mentality even though they went in behind at the break.
He said: "The mentality has been there for all to see this season. I reminded them at half time, I said: 'Get one goal and the game will change.' And it did. I thought after we scored they found it difficult and we were always on the front foot, and always looking to nick another one.
"I believe in the players, not just the quality they've got. The physicality again here was exceptional. They'll go hard until how ever long it takes to achieve what we want to achieve."
- Sports & Recreation