Goals from Jacob Bruun Larsen, Lorenz Assignon, Lyle Foster and Johann Berg Gudmundsson helped Vincent Kompany’s men on their way to a 4-1 win at Bramall Lane.
As a result, the gap to safety now stands at just three points with four games remaining.
Here’s how Burnley’s players rated:
5. Charlie Taylor - 7/10
Supported well down the left flank where he seemed to get a lot of space. Crosses in were much better too. Photo: Matt McNulty
6. Josh Cullen - 7/10
Made an important block early on when Burnley came under some pressure. Otherwise recycled the ball well and kept things ticking nicely. Photo: Matt McNulty
7. Sander Berge - 8/10
The pantomime villain on his return to Bramall Lane, with his every touch being booed. Quietened them down with a steady and mature display. Photo: Matt McNulty
8. Vitinho - 7/10
Brought some energy and workrate to the right-wing role. Could have got in on the act with a free header that was unfortunately too weak. Photo: Stu Forster