But it was disappointment for Cheltenham, who had striker Steve Guinan sent off in the closing stages for a late challenge on substitute Cliff Byrne.
By then Scunthorpe had already booked their passage to a home game with Wrexham in the next round.
Midfield man Ian Baraclough fired them in front in the 26th minute with an excellent curling shot from just inside the box into the far corner of the net.
It settled the home team down after Cheltenham had started brightly.
Grant McCann and John Melligan both went close for the visitors.
Scunthorpe were unable to find the high tempo they enjoyed when they produced their best performance of the season at home to Northampton Saturday.
"After that we found there was not much left in the tank," confessed caretaker manager Nigel Adkins.
"But this competition is all about winning matches and that is what we have managed to do."
But Cheltenham threatened an equaliser as they pushed forward strongly in the early stages of the second half.
Guinan should have done better when he got free into the box but finished with a poor shot.
Full-back Craig Armstrong went much closer in the 65th minute with a stinging drive that brought the best out of goalkeeper Joe Murphy.
But Scunthorpe kept chipping away at the opposite end and made the game safe in the 74th minute when leading marksman Billy Sharp raced free into the box for his 14th goal of the season.
In the closing stages, Scunthorpe might well have added to their score with Sharp, Andy Keogh and Richard Hinds all missing good openings.
Cheltenham assistant-manager Keith Douglas was full of praise for his players.
"We asked them to come here and be positive and they certainly were," he said.
"But unfortunately at the moment we lack a cutting edge in front of goal and are conceding too many poor goals at the opposite end."