United edged the first half and should have been in front when tidfielder Grant McCann fluffed a chance from close range in the 37th minute.
It was not until two minutes later that the visitors tested Scunthorpe's rookie goalkeeper Josh Lillis with a stinging drive from 20 yards.
Leeds stepped up the pace after the interval, but it was the home side who struck first when summer signing Gary Hooper exchanged passes with fellow striker Paul Hayes before steering a shot past goalkeeper Casper Ankergren.
Four minutes later Leeds were back on level terms when their summer signing Enoch Showunmi powered home a header from a free-kick curled into the box by Rob Snodgrass.
The visitors continued to dominate and it was no real surprise when last season's leading marksman Jermaine Beckford - making his first return to Glanford Park since a loan spell here two seasons ago - netted the winner in the 80th minute from a rebound after a shot from David Prutton had crashed against the bar.
In the closing stages only two fine saves from Lillis denied Leeds a further advantage, going full stretch to turn away efforts from first Jonny Howson and then substitute Luciano Becchio.
Yet Scunthorpe might have snatched an equaliser when Hooper forced his way into the box only to be denied by a good save from Ankergren.