The Clarets fell behind after Albert Adomah's 35th minute strike but hit back with second-half goals from Jason Shackell, Chris McCann and Martin Paterson.
In between Burnley's second and third goals, Lee Grant produced a terrific penalty save to keep out Steven Davies.
"That was as dominant a display as I have seen from us this season," Dyche said.
"We had 25 efforts on goal and I very much enjoyed our performance. We played with good ingenuity, organisation and freedom and even when we found ourselves behind at half-time we stayed calm.
"We always knew we could win the match. We made good use of the ball and managed the game well. All in all it was a very pleasing day for me, the team and the fans that backed us again and helped galvanise us as a group.
"I was really delighted with the way we went about our business but the madness of the Championship this season means that no-one can sit back and relax.
"Lee Grant made a fantastic penalty save but their goalkeeper made some top drawer saves too. After the penalty we went and scored again and that was a great way to respond.
"We have belief in what we do and we have seen through the anxiety of recent weeks."