Ben Mee's header moved Burnley five points clear of the bottom three with a 1-0 win over Sheffield United, who remain 11 points from safety.
Mee nodded in Robbie Brady's corner after 32 minutes to settle a game of few clear-cut chances at Turf Moor, with the plucky Blades again ruing a lapse in concentration in an otherwise largely even game.
Moments before falling behind they had come close from a corner of their own with Rhian Brewster denied on the line by Josh Brownhill's block, while David McGoldrick pulled a strong save out of Nick Pope five minutes after the interval.
Elsewhere, Aaron Ramsdale was in fine form to keep out efforts from Ashley Barnes and Chris Wood, but Mee - with only his fifth Premier League goal from 175 appearances - did enough to lift Burnley up to 16th, three points ahead of 17th-placed Brighton who have played a game more.
Burnley: Pope (7), Lawton (7), Tarkowski (7), Mee (8), Taylor (n/a), Brady (6), Brownhill (8), Westwood (7), Pieters (6), Wood (6), Barnes (6).
Subs: Benson (6), Stephens (6).
Sheff Utd: Ramsdale (7), Basham (7), Egan (6), Robinson (6), Baldock (6), Osborn (6), Ampadu (5), Stevens (6), McGoldrick (6), Brewster (6), Mousset (5).
Subs: Fleck (5), Burke (6), Norwood (6).
Man of the match: Ben Mee
Burnley hold firm to extend gap to relegation zone
Resurgent Burnley almost continued their upward momentum in the opening minute when Barnes took Wood's flick in his stride before pulling a strong save out of Ramsdale at his near post.
An early injury to Charlie Taylor took the wind out of the hosts' sails, and Sheffield United soon began to look their normal selves - but with their familiar struggles once they reached the Burnley box.
- Get Sky Sports | Get a Sky Sports Day Pass
- Premier League table | Premier League top scorers
- Premier League fixtures | Premier League results
On the half-hour mark they did come inches away from a breakthrough; Brewster's downward header was cleared off the line by Brownhill with Pope beaten, with the Clarets surviving to fight another day.
It was a cruel irony on the visitors that within moments they would fall behind to a corner at the other end, with Mee rising highest to beat Ethan Ampadu and power Brady's delivery inside the near post.
Brewster and Wood would exchange efforts before Burnley went in a goal to the good at the break, with the visitors still very much in the game - and they emerged for the second period looking like they knew it.
Five minutes after the restart McGoldrick came close to finishing off an intricate passing move but found Pope equal to his effort from a tight angle.
However, it took another 25 minutes for them to worry the goalkeeper again despite their territorial dominance, when George Baldock's drive was edged wide of his own post by James Tarkowski's sliding block.
Burnley changed to a five-man midfield to see out an important three points and, although they still allowed McGoldrick to head over from a corner in the dying minutes, they resisted Sheffield United's huffing and puffing to continue their comeback from their early-season form, and have now lost only one of their last six games.
What the managers said...
Burnley boss Sean Dyche: "I'm very pleased, it's an important result. We offered a different kind of performance, I don't think we were as good as we were against Leeds, but we got the result with our shape and our work.
"We thought it'd be a tight game, their scorelines have often been tight. We had a fair show of what we were about on Sunday in the first half, absorbing a lot of their play and creating one or two golden chances. We don't always make 20-30 chances, it's the quality of the chances."
Sheff Utd manager Chris Wilder: "We should do more, especially in the mid and final third. Late on they sat in, and worked their socks off which they do as a team, we struggled to find that space, find that pass that would get us back in the game.
"I'm saying the same thing again. It was a good start by them, they were the better team for the first 10 or 15 minutes, then we got a foothold and started to dictate and had a few opportunities. We got it into good areas where we want to get it into, but hitting the first man, not showing that bit of quality."
Man of the match - Ben Mee
It is easy to give the man of the match award to a goalscorer, but that would be harsh to overlook Mee's defensive output against a Sheffield United side who peppered the penalty area with 16 open-play crosses.
In addition to his goal, the centre-back won six aerial duels and only Ashley Westwood and Eric Pieters completed more passes for the hosts.
- Sheffield United are winless in their 16 Premier League games this season - equalling Queens Park Rangers' Premier League record of longest winless run from the start of a campaign (16 in 2012-13).
- Burnley secured consecutive home Premier League victories for the first time since October 2019.
- Burnley have won three of their last four home Premier League games (D1), as many as in their previous 13 combined (W3 D4 L6).
- Sheffield United have failed to keep a clean sheet in each of their last 19 Premier League games since a 3-0 victory against Chelsea in July.
- Sheffield United's Oliver Burke hasn't ended on the winning side in any of his first 25 appearances in the Premier League - the longest winless start to a player's career in the competition (overtaking Gareth Bale's 24 apps).
- Burnley's Ben Mee has scored his first Premier League goal at Turf Moor in 76 games since scoring vs Crystal Palace in January 2015. Four of Mee's five Premier League goals have been headers.
Both these sides are live on Sky Sports this weekend, with Burnley's home game with Fulham live on Sky Sports Premier League and Main Event from 2.30pm on Sunday; Kick-off at 3pm.
Sheffield United's trip to Crystal Palace 24 hours earlier is also live on Sky Sports Premier League and Main Event on Saturday from 2.30pm; Kick-off at 3pm.