Sheffield United had looked on course for automatic promotion when they went into April top of the table.
However, Monday’s reverse at Burnley was a fourth defeat in five and third away loss in a row as they paid the price of losing form at the worst time of the season.
With their top-two hopes over boss Wilder made six changes and he will have been pleased with how his much-changed side started in the West Midlands, as former Stoke man Tyrese Campbell went close early on.
The forward was then booked for simulation as he went down in the area under minimal contact from goalkeeper Viktor Johansson before the Blades took the lead.
Brewster’s deep corner took a deflection, bounced off the head of the unsighted Lawal, before McCallum bravely headed in under pressure from Wouter Burger.
Lewis Baker’s well-struck long range curler drifted just wide at the other end as the Potters, who made just two changes from the thrashing at Elland Road, looked to level before half-time.
Stoke fans grew increasingly restless as the second half wore on, with their side offering little in attack prior to Al-Hamadi’s introduction.
Cooper saved well from the Iraq international, though, and the Blades then scored a well-worked second three minutes from time to settle the outcome.
United opened the hosts up down their right and Sydie Peck’s low centre was converted at the back post by the on-rushing Brooks.
Striker Kieffer Moore, without a goal since 21 December, should have made it 3-0 in added time, but fired a finish over the bar.
Stoke, in 17th place, will hope the weekend results are enough to secure their survival before next week’s trip to fellow strugglers Derby, who are four points behind them with a visit to 20th-placed Hull on Saturday. Sheffield United host Blackburn before going into a play-off campaign.
