Iliman Ndiaye's second-half header secured all three points for play-off chasing Sheffield United against Cardiff City at Bramall Lane.
The Bluebirds had the best chance of the first half, when Max Watters' tame effort was saved by Wes Foderingham despite being clean through on goal.
Just two minutes after the restart, Morgan Gibbs-White found space down the left and crossed for an unmarked Ndiaye to head home from six yards.
Sander Berge had the chance to seal the win deep in added time, but his right-foot curling effort crashed back off the post.
The Blades stay in sixth place with victory, but extend their advantage over the chasing pack to four points.
Cardiff slip two places to 19th, but are already assured of Championship football next season; Peterborough joining Barnsley and Derby in League One next season after defeat to Nottingham Forest.
The visitors started strongly and Sheffield's back three looked shaky whenever the Bluebirds advanced.
Oliver Denham's long ball up to Jordan Hugill was smartly played first time to Watters, who beat the final defender only to fire a weak left-footed shot straight at Foderingham.
The Blades keeper almost gifted Cardiff the opener minutes later, his miss-kicked clearance hitting Watters on the edge of the 18-yard box but the Bluebirds striker could not control the ball.
Sheffield's first sight of goal came after 14 minutes, as Ben Osborn's low volley skipped off the surface but was well saved by Dillon Phillips in the Cardiff goal.
Berge's run from deep caught the Bluebirds defence sleeping as the hosts took control of the game, but Phillips was equal to the effort once more.
Berge had Sheffield's best chance of the first half, his neat spin freed him into the Cardiff box with Cody Drameh being treated for an injury, but once more Phillips was on hand to tip the effort around the post.
The Blades opened the scoring early in the second half when Perry Ng and substitute Mark McGuinness lost Ndiaye and allowed him to drift into space and power a header home.
That goal spurred on the hosts and lifted the home crowd, which had been quieter than usual during the first half as play-off nerves played their part.
Sheffield continued to run rings around the Bluebirds but despite their dominance they struggled to find any clear-cut openings.
A Will Vaulks long throw almost gave Cardiff an equaliser against the run of play, as Joel Bagan launched himself onto the end of it, but Foderingham stood tall to deny him.
Sheffield brought on the Championship's all-time leading goal scorer Billy Sharp as they searched for a second, and moments after coming on the veteran striker thought he had won a penalty, but referee Oliver Langford waved away appeals.
Cardiff improved in the final quarter of the match, Rubin Colwill's introduction making an impact, but the Bluebirds failed to carve out a clear opportunity to draw level.
The Blades almost made the points safe two minutes into added time when Berge was sent free by Sharp, his effort beat Phillips but the post came to Cardiff's rescue.
It did not matter though, as Sheffield held on to secure a crucial three points and keep play-off aspirations in their own hands.
Cardiff City manager Steve Morison told BBC Sport Wales: "I thought we were excellent, it was tough for us against a very good team.
"We started well and should have taken one of our chances, we didn't, and I'm gutted with the goal but it's shows how far we've come.
"We're doing the best we can with the group and I think there was some really good performances out there."
Sheffield United: Foderingham, Basham, Egan, Robinson, Osborn, Norwood, Fleck, Stevens, Berge, Gibbs-White, Ndiaye (Sharp 70'). Subs Not Used: A. Davies, Osula, B. Davies, Norrington-Davies, Uremovic, Hourihane.
Cardiff City: Phillips, Ng, Nelson, Denham, Drameh (McGuinness 46'), Bagan, Doyle, Ralls (Vaulks 46'), Wintle, Hugill, Watters (Colwill 66'). Subs Not Used: Luthra, Flint, Harris, Ikpeazu.