The Championship leaders scored twice in the last minute to beat 10-man Rotherham and extend their winning run to 16 games.
The two goals were scored at the same time 10 minutes into 13 added on atTurf Moor.
Ben Wiles had nodded the Millers into a shock early lead, only for Jay Rodriguez to level the score.
Cohen Bramall was sent off for two yellow cards within seven minutes of Chiedozie Ogbene's return to the game.
The Belgian substitute played a big part in the winner, as well as the goal, which was scored by the on-loan forward.
Josh Brownhill was on the receiving end of the fine run and pass from the winger and although his shot was saved, he was on hand to tuck home the winner.
Despite their lofty position, the side are not doing things the easy way despite their recent victories.
They needed a last-second winner to beat Reading on Saturday. They needed a late goal to beat Norwich in their last game, after a comeback from 2-0 down to win 4-2 at the Stadium of Light.
With entertainment high on the menu and a healthy gap opening up to a number of challengers who seem unable to put consistent runs together, hopes of an immediate return to the premier league are growing.
They will consider themselves unfortunate to come away empty-handed from a game in which they played a full part until the final whistle.
They were on the defensive for a long time after Wiles scored.
There was a chance for Washington to double the lead, but his 20-yard left-footed strike was pushed aside by Muric.
Rodriguez's goal was a fine one, as Nathan Tella hooked the deep cross back to him, and he headed in from close to the goal line.
It was very much against the run of play after Rodriguez and Tella both saw efforts cleared off the line, and after Johansson saved a Gudmundsson volley in the second half.
However, even though he was already on a booking, he lunged in on Roberts to giveBurnley the initiative.
The Clarets needed to rescue not just one point but all three in order to keep their perfect home record intact.
The boss of the club told the radio station.
It was good for the team, good for the fans, and it gave us a little bit of something before the big game.
We were unlucky not to score more because we were doing what we do and we were lucky that the goals came in the last minute.
It shows a bit of maturity because it's a group that's coming together and you have to be able to look each other in the eye and stay calm.
Matt Taylor spoke to the radio station.
The players deserve something to show for their hard work.
"You need a little bit of luck and a little bit of help from the officials, just for them to make the right decisions and that certainly didn't happen tonight, but I don't want that."
In a game where there were very few moments where the referee was going to go to his book, the first booking was cheap. Cohen can't give the ref an option, an opportunity or a decision to make on the second when it's happened in such a short time. The moments that didn't go our way were the ones that he was learning the game from.
"Tactically, I thought we were excellent, we scored two good goals and we had other good moments in front of goal but ultimately we are standing here pleased with the performance but with nothing to show for it."
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