Young striker Joe Parker, formerly of Gloucester City, put the Welsh club ahead in the 20th minute.
The lead was doubled by Kieran Parselle two minutes into the second period and ex-Robins loan forward Shaun Jeffers made it 3-1 in the 87th minute.
Joe Hanks pulled a goal back for Cheltenham from the penalty spot in the 90th minute.
A quartet of trialists featured for the Robins: Defender Luis Morrison-Derbyshire, Croation forward Tomislav Ivicic, ex-Hereford midfielder Sam Bobes and Algerian striker Mehdi Kerrouche.
Kerrouche, 29, has previously been on the books of Oxford United and Swindon Town, scoring eight goals for the Wiltshire Robins during their League Two title winning campaign of 2011/12.
The result leaves Cheltenham's second string without a point from three Southern Group B fixtures, having suffered defeats by Portsmouth and Bristol City earlier in the season.
Cheltenham Town Reserves: H Reynolds, Deaman, Bowen, Hanks, Rowe, Morrison-Derbyshire, Kerrouche (Page 67), Bobes (Daly 83), Ivičić (Lawrence 51), Dale, Haworth. Other sub: Craddock.