The rock-bottom Blades will play in the Sky Bet Championship next term after Willian Jose’s second-half winner.
Under caretaker boss Paul Heckingbottom, United are 19 points from safety with six games remaining and have won just four times all season.
The Blades have lost 26 of their 32 games, having finished ninth last term, with their two-year stay in the Premier League over.
They rarely looked like earning a stay of execution, although Enda Stevens was denied by Rui Patricio.
Mid-table Wolves also struggled to find serious momentum in a forgettable game but Oliver Norwood did head Willy Boly’s fortunate first-half effort off the line.
Newcastle’s late win over West Ham earlier in the day left United needing to avoid defeat to delay their inevitable return to the second tier.
There was little intensity from the visitors in a drab first half though, and Wolves came closest to an opener after 21 minutes.
Rayan Ait-Nouri’s corner was chested down by Jose and John Egan’s clearance ricochet off Boly’s heel to loop towards goal, only for a combination of Norwood and the crossbar to keep the ball out.
Daniel Podence’s half-volley flew over after half an hour but Wolves - firmly stuck in mid-table - failed to convince they would break the monotony.
The biggest flashpoint came nine minutes before the break when Ait-Nouri was lucky to avoid a red card.
The defender landed on Rhian Brewster’s ankle when trying to shield the ball but VAR did not intervene and it was Brewster who was booked for the challenge.
The game meandered into the break and there was nothing to suggest the scoreline would change during a low-key start to the second half.
Yet, belatedly, United did conjure their first chance of the game after 59 minutes - only for it to lead to Wolves’ winner.
Brewster’s low cross found the unmarked Stevens and his low strike was blocked by Nelson Semedo.
Immediately, Wolves broke with Semedo and Podence combining to send Traore away. He then breezed past Egan for Jose to sweep in his first Wolves goal from six yards.
Stevens’ quick turn and shot forced a good save from Rui Patricio as United woke up but it was too late.
Aaron Ramsdale denied Romain Saiss from point blank range with seven minutes left.
Fabio Silva then shot straight at the goalkeeper and Traore sliced wide on the break as time ran out on United’s top-flight stay.
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