Crawley Town suffered their second successive defeat of the new league campaign when Mohamed Eisa headed in a 38th minute winner.
Head coach Harry Kewell made just one change to the line-up from last Saturday’s opening game defeat against Port Vale.
Josh Payne came in for Josh Yorwerth, who was on the bench.
Panuche Camara and Aryan Tajbakhsh both came in to the squad on the bench but there was no place in the squad for Dean Cox.
Reds came close to taking the lead as early as the sixth minute when Mark Randall fired straight at keeper Jon Flatt, on loan from Wolves, at the end of a nice run.
Enzio Boldewijn found Lewis Young whose effort from the far side was saved.
Jordan Roberts went on a lovely run before shooting, only to be denied by Flatt.
Eisa gave the Robins the lead seven minutes before half-time with a straight-forward header from a fine Kyle Storer cross to score his fourth goal of the season.
In the second half Roberts set-up Boldewijn with a chance but he blasted off-target.
It looked like Reds had equalised on 57 minutes when Thomas Verheydt bundled Mark Connolly’s header in the net but the referee awarded a free-kick.
Cheltenham’s Carl Winchester threw himself at the back post to deny Boldewijn.
Young played a great cross towards Verheydt but it was intercepted for a corner.
Connolly looked to net an equaliser but was denied on the line by Jordon Forster.
Connolly hit the crossbar but there was no-one on hand to put away the rebound.
Tuesday’s night’s scorer against Birmingham in the Carabao Cup, former Dulwich Hamlet striker Camara came on for Verheydt on 72 minutes for his Football League debut.
Camara immediately helped create a chance when he found Cedric Evina who squared to Harrold who volleyed wide.
On the closing stages Connolly pushed forward but put Randall’s pass off-target.
Then Randall put a ball in the area but it missed all his team-mates.
REDS: Morris, Young, Connolly, Lelan, Evina (Lewis 85), Payne (Harrold 64), Bulman (capt), Randall, Boldewijn, Verheydt (Camara 72), Roberts
Unused subs: Mersin, Blackman, Yorwerth, Tajbakhsh, Lewis
Cheltenham: Flatt, Grimes, Cranston, Storer (capt), Pell, Wright (Graham 68), Winchester, Boyle, Sellars (Atangana 27), Eisa, Forster
Unused subs: Holman, O’Shaughnessy, Page, Bower, Lovett
Referee: Scott Oldhan
Attendance: 2,384 (85 away)