A penalty from Sory Kaba put Cardiff in front, but James McAtee levelled for the Blades before the break.
Sheffield United pulled clear in the second half through goals from Jack Robinson, Iliman Ndiaye and Ciaran Clark to leave 21st-placed Cardiff firmly in the fight to avoid relegation from the second tier.
Manager Paul Heckingbottom's side sit five points clear of third-placed Luton, who were 2-0 winners at Rotherham to extend their unbeaten run to 10 games.
"The fact we won 4-1 after going behind shows a lot about the group," Heckingbottom said. "It's not the first time in recent weeks.
"We have put ourselves into a position where it's about us. Every time we win the margin of error gets tighter for the teams chasing us."
Championship leaders Burnley last week secured promotion back to the top-flight a season after dropping out of the EPL but were held to a goalless draw on Saturday by managerless Reading.
Fifth-placed Millwall maintained their playoff push with a 2-0 victory over Preston thanks to goals from Tom Bradshaw and Zian Flemming.
Blackburn, in sixth, were held to a goalless draw at home to Callum Elder's Hull, while Coventry moved to within a point of the final playoff spot with a comfortable 3-0 win at QPR.
Viktor Gyokeres scored either side of a Gustavo Hamer goal for Coventry.
Relegation-battlers Blackpool moved to within four points of safety as Jerry Yates' early goal proved enough to beat bottom side Wigan.
Huddersfield remain firmly in the relegation battle - sitting a point clear of the bottom three after losing 1-0 at Swansea.
Jayson Molumby scored twice as Tom Rogic's West Brom came from behind to pick up a rare away win at Stoke.
West Brom secured their 2-1 victory after Jacob Brown had opened the scoring for the hosts, who had midfielder Ben Pearson sent off in stoppage time.
Sunderland also ended with 10-men, but still beat Birmingham 2-1, goals from Denver Hume and Amad Diallo cancelling out George Hall's opener for the Midlands club.
Elsewhere, Watford beat Bristol City 2-0 at Vicarage Road thanks to an own goal from Harry Cornick and Joao Pedro's second-half strike.
10°C