Jacob Bruun Larsen, Lorenz Assignon, Lyle Foster and Johann Berg Gudmundsson scored the goals for Vincent Kompany's side, who have moved onto 23 points from their 34 league matches this season.
The Clarets remain 19th in the table, but they are only three points behind 17th-placed Nottingham Forest, while Sheffield United stay bottom, 10 points from safety, with Chris Wilder's side seemingly heading back down to the Championship.
Burnley have now lost just one of their last seven league matches, but it is back-to-back defeats for Sheffield United, who were also beaten at Brentford last time out.
Burnley pick up huge win in their fight against relegation
Oli McBurnie should have sent Sheffield United ahead in the ninth minute when he was presented with an opportunity from point-blank range, but Burnley goalkeeper Arijanet Muric made a smart save.
Muric was again called into action 10 minutes later to keep out an effort from Ben Brereton Diaz, before Ivo Grbic did well to keep out a deflected effort from Foster down the other end.
Burnley's goalkeeper made a smart stop to deny McBurnie just past the 30-minute mark, and it then proved to be an excellent finish to the half for the visitors.
The Clarets made the breakthrough in the 38th minute of the clash through Larsen, with his effort taking a big deflection off a defender before rolling into the bottom corner of the net.
Two minutes later, it was 2-0, with Assignon working his way into the away side's penalty box before finding the back of the net with a low finish, and the two goals summed up Sheffield United's campaign.
Muric made another excellent stop early in the second half to keep out an effort from James McAtee, but Sheffield United did manage to register in the 52nd minute.
Sheffield United suffer 23rd Premier League loss of the season
The goal came from Gustavo Hamer, with the midfielder working his way into the Burnley box before placing an excellent effort into the far corner, and it was very much game on at that stage.
However, Burnley netted a third in the 58th minute following smart work from Assignon, who delivered an excellent cross into Foster, and the attacker carefully placed the ball into the bottom corner of the net.
It went from bad to worse for Sheffield United in the 71st minute, when Gudmundsson, who had only just entered the field, curled a brilliant effort into the back of the net to end the match as a contest.
Gudmundsson came close to scoring again shortly after, thumping a volley against the post, before Jayden Bogle was denied by Muric late on, with the relegation six-pointer finishing 4-1 to the visitors.
Both teams will face Manchester United in their next match, with Sheffield United heading to Old Trafford on Thursday night, before Burnley visit the 20-time English champions next weekend.