The Iron gave a surprise debut to midfield man David Syers, on loan from Doncaster, whose arrival was kept quiet until an hour before the kick-off.
They were a goal ahead after six minutes when winger Etienne Esajas rifled home a left foot shot from the edge of the box after the ball had been chested into his path by striker Deon Burton.
Scunthorpe continued to make chances throughout the first half against an unconvincing Cheltenham defence - but could not find their finishing touch again.
Syers twice let himself down with wayward finishing, as did striker Jamie Spencer, making his full league debut for the home side, on loan from Huddersfield.
The visitors did begin to force their way into the game before the interval but the best they could muster was a long-range effort from Terry Gornell which finished well over.
Cheltenham continued their improvement at the start of the second half and veteran striker Jamie Cureton came off the bench only to miss a golden chance to equalise on the hour with a weak shot from six yards straight at keeper Sam Slocombe.
At the opposite end it was Syers and substitute Sam Winnall who both squandered other great chances to help Scunthorpe breathe more easily, before the latter finally did make it 2-0 in the 90th minute with a shot from 12 yards.