The game was decided four minutes after half-time when midfielder Brian Wilson drove in a shot from the edge of the box to make it only one defeat in the last 12 games for John Ward's men.
However, visitors Chester dominated the closing stages and had chances to at least draw level.
Next month the two teams will meet again in the FA Cup third round and on the evidence of this encounter, it should be another close game.
In the first half it was the home side who played the more enterprising football and they must have been disappointed not to take a lead into the break.
Grant McCann in the centre of midfield and wide players Wilson and JJ Melligan were prominent as the Robins created a series of promising openings without finding the final touch.
Steve Guinan poked a shot just wide after 10 minutes, Kayode Odejayi saw a shot saved by on-loan goalkeeper John Ruddy and it was the Everton youngster who again rescued his team with 20 minutes played when he dived bravely at the feet of Melligan.
Chester relied on set plays for their best chances of the first half and Cheltenham goalkeeper Shane Higgs held shots from Ryan Lowe and Stewart Drummond, then got down to block a low drive from Ben Davies shortly before the break.
After taking the lead Cheltenham appeared to sit back and invite Chester onto them, defending deeper and deeper as the game wore on.
Davies and Lowe both missed good chances to level for the visitors, although substitute Damian Spencer had a great chance to score another for Cheltenham at the end.
He broke clear of the City defence but once again Ruddy was out quickly to block his shot.
Cheltenham survived a nervous ending to the game to claim three points that sent them back above Chester in the League Two table.