It came after substitute Daniel Webber looked like salvaging the Blades a point with two goals in four minutes late in the game.
But Scunthorpe deservedly got their reward for a battling performance that cut the big-spending Baldes down to size.
The home side thought they had gone in front after 19 minutes when Martin Paterson steered an angle shot at goalkeeper Paddy Kenny, only to see it controversially flagged offside.
Sheffield's £2million summer signing, Billy Sharp, returning to the club where he scored 56 goals in two seasons, struggled to make an impact.
It was Scunthorpe who took the lead in the 37th minute when skipper Andy Crosby powered home a left-foot volley after a free-kick had been flicked on by Sparrow.
At the opposite end Sheffield went close with a stinging 20-yard drive from Chris Armstrong that was just a shade too high.
But Scunthorpe increased their lead in the 62nd minute when Paterson was put clear by substitute Jonathan Forte and raced into the box to tuck his shot past Kenny for his fourth goal in successive games.
Scunthorpe looked in complete control and Forte went close with a header.
Sheffield's fightback started in the 79th minute when the home defence could not clear a high ball into the box and Webber flicked a close-range header past goalkeeper Joe Murphy.
Four minutes later Webber struck again when he fired home from close range after a good knock down into the box by striker James Beattie.
Suddenly it was Sheffield pressing forward strongly in search of a winner, but it was Scunthorpe who snatched it as the game entered stoppage time.
Kevan Hurst lifted a high ball into the box which Forte nodded down and Sparrow forced his shot home from close range.
There was further drama when both teams finished with ten men, with Sheffield defender Derek Geary and Scunthorpe full-back Cliff Byrne both red-carded by referee Keith Stroud after going head-to-head following a challenge.