The 24-year-old was dropped to the bench in favour of Martin Paterson, but got his chance when the latter had to be taken off with a hamstring injury shortly before half-time.
Treacy hit the opening goal just after the hour mark, and it was his cross which Lewis Buxton handled to give away a penalty that Ross Wallace converted to complete the scoring.
The former Blackburn and Preston winger hit the post in stoppage time, and Dyche was delighted with Irishman's performance against the club he appeared for on loan at the end of last season.
"It's good to see him enjoying his football," said Dyche, who was pleased to see the Clarets collect only a second win from their last eight games.
"He showed moments here - I think there's more to come. Whenever he gets a chance to play that real match fitness and sharpness will come. It's not a given - you've got to earn the right to play out there.
"He was a very young, really well-thought-of talent at Blackburn. One or two snags along the way, but he has that moment of quality, that inner belief to deal with the ball on nearly every occasion. He's one who wants the ball all the time and I'm pleased to say we've got several of those at this club.
"It was a very good away performance for any day," added Dyche. "I thought the lads were very thorough in what they did."