The result means that Yeovil are not out of the danger-zone, despite their recent good run of form, which came to an end thanks to a 51st-minute goal from Frankie Artus.
The on-loan Bristol City youngster benefited from a neat bit of skill from winger David Hutton, who cut inside from the right and struck a low, firm shot against the base of Yeovil goalkeeper Chris Weale's left-hand post.
The ball rebounded out to Artus on the edge of the penalty area and he swept in his third goal in five matches to bring an end to Yeovil's run of 502 minutes without conceding a goal.
Earlier on, Yeovil had started the game brightly and Gavin Tomlin got into two good positions within the first ten minutes but on both occasions he was unable to beat goalkeeper Scott Brown in the Cheltenham goal.
After that early flourish the game settled into a drab, colourless pattern with both sides showing why they have been anchored in the bottom half of the table all season.
Passes went astray, clearances were unceremoniously thumped anywhere and scoring chances were at a premium.
Artus sliced a shot wide for Cheltenham on the stroke of half-time but things improved in the second half.
Tomlin appeared to be Yeovil's best chance of creating a goal and he almost did so on 70 minutes when he produced a clever piece of skill on the edge of the area before smacking a shot against a post.
Yeovil continued to plough forward despite having midfielder Gary Roberts sent off for a second yellow card in the 77th minute but they were unable to find a way to goal.
Cheltenham held on to make it only two defeats in their last ten games, although they remain ten points away from League One safety and relegation seems a certainty.
Judging by the young age of this Cheltenham team however, planning for the future is already well underway.