Burnley's unbeaten home record in the Sky Bet Championship appeared under threat at Martyn Woolford put struggling Millwall in front after 27 minutes.
But the visitors' lead last just two minutes as Ings grabbed his first of the game, turning in the box before curling past the helpless Stephen Bywater.
Ings should have doubled the home side's lead but after he was fouled by Nadjim Abdou in the box his penalty was saved by Bywater - although Burnley did go into half-time ahead as Dean Marney unleashed from 25 yards just before the break.
And Ings did have his second as he made the game safe on 62 minutes, leaving Dyche left to hail his side's attacking qualities.
"We put some real good quality into the final third," he said. "We have got a strike force to be reckoned with but the front six, if you like, were excellent in their play.
"There was no disappointment when they scored and we kept playing and picked up where we were before the goal. It was a very defensive set-up from them.
"Ings has real quality, and the pass for the second goal as well was great. Ings is a player who can score all types of goals.
"We want to play mixed football which is what we are doing, we want that freedom.
"I have made it clear on several occasions that if you get the performance level right then it attracts wins.
"There have been some fantastic markers this season. But I believe in development for all, myself included.
"We are relentless in our attitude in training and as long as that relentless mentality is there as a collective then we can get the results. I believe in development for all, myself included."
The result means Millwall have won just once in their last 11 games and manager Ian Holloway insists he wants his Lions to follow in Burnley's footsteps.
"That was very disappointing to be honest," Holloway said. "The important things need to start happening for us.
"We play to get ourselves in front and we did that but what we are not doing is holding on. We had a game plan to stop (Sam) Vokes and Ings which worked at the start for us.
"We need to get breaks quickly because that dressing room is low. We can learn from the infrastructure that Sean's team had.
"Sean is a modest man but he will be buzzing inside. It is tiny tiny margins we are talking about like two to three yards.
"But good luck for the rest of the season to them, if there is anybody with a stronger mentality than them I would like to see them but hopefully not to soon."