The Clarets skipper leapt above Cristian Romero to guide Josh Brownhill's set-piece past Hugo Lloris in the 71st minute.
Sean Dyche's side, who beat Brighton and Hove Albion at the weekend, have moved within a win of safety as a result with games in hand on their rivals.
Here are the ratings.
Here are the ratings.
5. Ben Mee 8.5
Illustrated an unstoppable desire to beat Romero to Brownhill's set-piece to score the winner. The skipper, who was outstanding in both boxes, had earlier threatened when connecting with McNeil's free kick and almost added a second when given two bites of the cherry late on. Photo: Alex Livesey
6. Aaron Lennon 7.5
Continues to belie his years with his pace, work rate and ground coverage. Perhaps not quite as instrumental as the game at Brighton, but more than played his part. Didn't give Sessegnon a sniff and put in a shift in support of Roberts to keep Son on the periphery. Photo: Mike Hewitt
7. Dwight McNeil 8
When McNeil shines, so do Burnley. The winger dazzled on the ball, skating across the pitch effortlessly, and completed his duties defensively. The former Young Lion wowed the crowd with a spectacular piece of skill to beat three men in the second half and delivered delightful crosses for Mee and Rodriguez. Photo: Stu Forster
8. Josh Brownhill 8.5
His performances have sky-rocketed in recent weeks. The midfielder is playing out of his skin, his confidence is through the roof, and he's proving a real asset. Ran his socks off, made key interventions and was economical in possession. His delivery for Mee's winner was perfect and we can't forget the turn that floored Bentancur! Photo: Charlie Crowhurst