Danny Webber looked to have rescued a point for Bryan Robson's side with two goals in four minutes late in the game.
But local boy Sparrow diverted a loose ball home at the far post in the 90th minute to secure a deserved three points for Nigel Adkins' side.
Scunthorpe skipper Andy Crosby smashed home a volley at the far post to give Scunthorpe a half-time lead and Martin Paterson held his nerve to fire a second after the break.
Webber, a second-half substitute for Keith Gillespie, then headed home his first in the 79th minute and hauled the Blades level with another four minutes later.
But Sparrow had the last laugh, sending Robson's side crashing to a second league defeat in four matches and ensuring a miserable return to Glanford Park for Blades striker Billy Sharp.
Scunthorpe's Cliff Byrne, a rock at the back, and Blades defender Derek Geary were sent off following a tussle in the closing stages.
Sharp received a warm reception from the home faithful on his first return to Scunthorpe, while former Bramall Lane academy team-mate Kevan Hurst retained his place in Nigel Adkins' side.
Player-coach Ian Baraclough and on-loan Charlton defender Kelly Youga were recalled by Adkins, while Robson reverted back to the side that kicked off against West Brom last week.
Hurst almost gave Scunthorpe a dream start after hesitancy in the visitors' defence, but he dragged a low left-foot shot wide.
The Blades responded and Sharp wasted a gilt-edged chance to notch his first goal of the season, his tame volley from Leigh Bromby's cross comfortably gathered by Joe Murphy.
A jittery Blades defence were given a real scare in the 18th minute when Martin Paterson pounced on a mistake by Nick Montgomery to rifle his shot inside the far post, but his effort was ruled out for offside.
The close proximity of the crowd and Scunthorpe's no-nonsense approach clearly rattled Robson's side.
Murphy had to be at his best when Sharp controlled Geary's knockdown and turned to fire in on goal.
But the Iron took a deserved lead in the 38th minute. Baraclough's free-kick found skipper Crosby at the far post and his left-foot volley thundered into the roof of the net.
Matt Sparrow went close to doubling the home side's lead in the 57th minute with a rising 20-yard shot.
Paterson then turned Matt Kilgallon to curl in a shot, but did better moments later when substitute Jonathan Forte, another former Bramall Lane product, found the striker with a fine defence-splitting pass - his first touch after replacing Paul Hayes.
Paterson outpaced Blades skipper Chris Morgan before coolly slotting the ball beyond Kenny.
Substitute Cleveland Taylor almost cashed in on more slack Blades defending, but Kenny clawed his hooked effort away before Robson sent on Jon Stead and Alan Quinn for Chris Armstrong and Sharp.
The visitors then cut the deficit out of the blue. Beattie headed on Geary's free-kick and Webber, a 61st-minute replacement for Gillespie, raced in at the far post to head the ball home.
The Blades then levelled with seven minutes to go when Webber toe-poked home another Beattie flick-on from Michael Tonge's ball in.