Clarets boss Sean Dyche felt the 2-0 victory over Rotherham was a "really important and big win".
A first half penalty and late clincher from Scott Arfield earned Burnley another three points, as they climbed to second place in the Championship, jumping into the automatic places for the first time since November.
It was a ninth league game without defeat, and Dyche said: "It was hard work, with Neil (Warnock) being Neil, he's got a new group, players back who haven't been figuring, they've got that bit of fervour, coming here thinking its kind of one with no expectation on them, and tried to play on that.
"They got the ball forward constantly, early, broke the game up and it was a disjointed game, but I like the fact we can win games in different ways, and we've won it in a different way again, and rightly in end if you look at the chances we created, it's fair to say we deserved it."
Joe Newell had a great chance to level matters with 11 minutes remaining - Rotherham's only clear sight of goal - and Dyche admitted: "It's hard to keep teams to no chances, no matter who you're playing, and it was a good chance, but we'd had six or seven by that stage, got a penalty, which looked the right decision, and actually I thought there was a clearer penalty with Michael Keane dragged to the floor.
"We didn't get that one, but scored a fine second goal and the work is done.
"Overall I was really pleased, that was a really important and big win.
"I've said it many times, sometimes the hardest fight to win is the one you're expected to, and we've taken care of business well."
Keane picked up a head injury when pulled down by Kurt Broadfoot in the aforementioned incident, and £3m centre back James Tarkowski replaced him to make his Burnley debut.
Dyche said: "Keano's ok, he didn't go out, he just felt a little bit off, and they are more diligent with head injuries these days, rightly so.
"It was a precaution, so the medical team will check him out.
"Tarky done well and Ben Mee was outstanding - when the ball comes forward that often, you've got to deal with it, and he was like a head on a stick.
"The ball is coming forward a lot, it's disjointed, they're trying to work for throw ins and free kicks, it keeps coming in your box, and he was good. It will be good for him to get his first win, albeit in strange circumstances.
"Joey (Barton) and Jonah (David Jones) were both good, the centre halves, Keano and Ben and then Tarky and Ben, were outstanding, it's a hard game to play. Boydy (George Boyd) was ill last night and did fantastically well physically. I would have got him off earlier but he was playing so well.
"He was poorly but managed to eat and get a night's sleep, so there were some good signs about the mentality of the group, the honesty and endeavour, and add in the quality and it's a good mix."