The win was just Sheffield United's third in the league this term, and it moved them onto 13 points in the table, now level with 19th-placed Burnley and seven behind Luton in 17th.
Chris Wilder would have been looking for a response from his players following the 5-0 home loss to Aston Villa last time out, and it was an impressive showing from the Blades at Kenilworth Road.
Sheffield United had an opportunity to make the breakthrough inside the first two minutes through James McAtee, but his low effort was just wide of the far post.
Luton were next to come close in the ninth minute through Gabriel Osho, but his header from a corner was always moving wide of the post.
The visitors made the breakthrough in the 30th minute of the contest through Cameron Archer, who swept the ball into the corner of the net with a composed silence to silence the home supporters.
Sheffield United's second of the match came from the penalty spot in the 36th minute, with McAtee keeping his cool after a handball from Luton's Reece Burke, with the decision given by the referee after checking the monitor following advice from VAR.
Luton had a penalty of their own early in the second period, with Vinicius Souza penalised for a handball, and Carlton Morris stepped up to halve the deficit in the 52nd minute.
Sheffield United goalkeeper Wes Foderingham made a brilliant save to deny Morris 20 minutes from time, with Luton pushing for a leveller in front of their own supporters.
The visitors managed to score a third in the 72nd minute through Souza, though, with the Brazilian expertly picking out the far corner to give his side breathing space.
Luton had chances late on, with Elijah Adebayo having a shot blocked in the 78th minute, before Tahith Chong missed the target with an attempt five minutes later.
Andros Townsend also brought a smart save from Foderingham late on, but there was a chance for a fourth for Sheffield United in the final moments, with Rhian Brewster finding space in a dangerous area, and his effort flew wide of the post.
Luton had been on a six-game unbeaten run in all competitions ahead of the contest but were undone by the team at the bottom of the division on Saturday afternoon.