A first half Victor Adeboyejo goal was enough to see Bolton Wanderers take all three points from the Robins at the Toughsheet Community Stadium.
Darrell Clarke's side put on an impressive showing but just couldn't find a way to get themselves back into the game after going a goal down.
After full-time, Clarke said:
"It was a decent performance, we should of got more but we didn't get more. But we come to a team that's right up there and we're on the front foot for a lot of the game.
"I enjoyed a lot of aspects of our performance but not the scoreline.
It was the hosts who came the closest early on when the ball fell nicely for Dion Charles in the area. He smashed an effort at goal only to be foiled by the strong hands of Luke Southwood.
Town responded well however and brought Trotters keeper Nathan Baxter into action just moments later, as he got down well to his right stopping Rob Street's shot on goal.
A flurry of chances followed for the visitors, as Tom Bradbury saw his header blocked off the line before Tom Pett saw an effort from range go over the bar.
The Robins midfielder came even closer on 20 minutes, this time seeing his volley bounce just wide of the near post.
But despite the chances it was the hosts who hit the front just before the 25-minute mark. A mistake from Bradbury at the back allowed Adeboyejo to race in on goal and net the opening goal of the game.
It could have easily been level at the break had Baxter not been on hand to once again prevent the Robins from finding the net. This time it was George Lloyd who was kept at bay from close range at the back post.
Into the second half and the Robins set about getting back into the clash right away, as Lloyd picked out Street in the area only for his header to be comfortably held.
Clarke's side had the ball in the back of the net on 54 minutes but this time it was the referee who's call kept the hosts ahead.
Lloyd's original header was saved before he poked in the follow up, only to be penalised for what looked like a tight offside call.
Elliot Bonds gave Baxter a scare not long after the hour mark when he took aim from range, but the Bolton keeper was lucky to see the strike hit the side netting.
The Robins kept pushing and very nearly equalised in injury time, but some bodies on the line defending stopped substitutes Josh Harrop and Nathan Butler-Oyedeji's efforts from hitting the back of the net.
Kyle Dempsey nearly made it two for Bolton on the break right at the death but lost his footing in the area as he went to pull the trigger.
BOLTON WANDERERS (3-1-4-2): Baxter; Toal, Santos (C), Iredale; Sheehan; Dacres-Cogley, Thomason, Maghoma (Dempsey 75), Williams (Ashworth 88); Adeboyejo (Jerome 80), Charles (Bodvarsson 75). Subs not used: Coleman (Gk), Morley, Matheson
CHELTENHAM TOWN (3-5-2): Southwood; Davies, Bradbury (Butler-Oyedeji 68), Freestone; Long (C), Bonds, Sercombe (Harrop 77), Pett, Ferry; Street (Keena 68), Lloyd. Subs not used: Pardington (Gk), B.Williams, Thompson, Smith
REFEREE: B Speedie
ATTENDANCE: 19,309