For Town,as expected, Jake Lawlor replaced the suspended Will Smith in the home defence.
Cheltenham made the better start without causing the Town rearguard any problems, before Town began to hit back.
Aaron Martin won a corner which was easily cleared and then the Robins’ keeper, Josh Griffiths did well to snatch a Warren Burrell cross off Martin’s head.
But it was the visitors who were now looking the more dangerous and Lawlor had to clear an Andy Williams shot off the line to prevent them taking the lead.
Next, Alfie May broke through outpacing Lawlor and Connor Hall, but drove his shot well over the bar.
However, on 43 minutes, the Robins scored the only goal of the game when the Town defence failed to clear their lines and Sean Long chipped to the far post for Will Boyle to beat Belshaw with a header into the far corner.
After the break, Town took the game to the Robins, but couldn’t penetrate their defence in depth.
On the hour, an excellent cross from Ed Francis provided a chance for Martin, but he headed straight at Griffiths.
Simon Weaver brought on Ryan Fallowfield and Jack Muldoon to replace Burrell and Josh McPake with fifteen minutes left.
With five minutes to go, a Connor Hall header from George Thomson’s free kick sailed across the face of the goal and just missed the far post.
In a last ditch gamble, Josh Andrews was brought on for the last few minutes, but there was to be no late equaliser for Harrogate and Cheltenham’s league experience saw them through to victory.
Belshaw,Burrell(Fallowfield 75),Francis,Lawlor(Andrews (89),Hall,Smith,Falkingham,Thomson,Power,McPake(Muldoon 75),Martin,March.
Griffiths,Hussey,Tozer,Raglan,Thomas,Clements(Long 29),May(Vassiliev 80),Blair,Williams,Boyle,Azaz(Sercombe 80).
By John Harrison.