The Blades wasted a golden opportunity to go ahead on 11 minutes when Harrison Burrows squared to Patrick Bamford who was unmarked after Dom Hyam slipped, although the striker guided his effort wide from close range.
And after Adam Davies made a routine save to deny Windass, Burrows failed to hit the target after being picked out by Callum O’Hare.
It typified a wasteful opening half from the home side, and having survived those scares, Wrexham almost punished the Blades as Issa Kabore’s floated cross was nodded narrowly wide by Lewis O’Brien.
When Gus Hamer finally managed to beat goalkeeper Arthur Okonkwo from Jairo Riedewald’s cross, Wrexham were rescued by the offside flag as they kept themselves in the contest going into the second half.
The Red Dragons thought they had stunned Bramall Lane when Windass drilled beyond Davies 16 seconds after the restart, only for the offside flag to deny them the opener.
And Wilder’s men went in front just minutes later as, after Okonkwo kept out Bamford’s strike, Brooks was on hand to rifle the rebound into the net for his sixth goal of the season.
But Windass got his moment in the limelight as he was picked out by Smith before coolly slotting into the net in front of the travelling supporters.
It triggered an improved spell for the Welsh side who took the lead 12 minutes from time as Kabore’s cross was headed into the net by Smith – his eighth goal of the campaign across all competitions.
Brooks and Tom Davies both missed the target with efforts late on as Wrexham went into the international break on a high having earned a 17th league win of the campaign – earning a first league double over the Blades in the process.