A mistake by veteran defender Jamie Victory 10 minutes into the second half handed the points to Port Vale and maintained their 100 per cent record in Coca-Cola League One.
Cheltenham Town's longest serving player mis-hit a back pass to goalkeeper Shane Higgs and Vale striker Leon Constantine nipped in to score with a cool finish.
Clear scoring chances were few in an even first half with both sides defending solidly and unable to get their quick front players in behind the respective back fours.
Cheltenham's JJ Melligan was a lively presence down the right-hand side and he saw a powerful shot parried by goalkeeper Mark Goodlad after 15 minutes.
Port Vale hit back and Akpo Sodje wasted arguably the best chance of the half shortly afterwards.
Collecting a pass from Constantine, the former Darlington man found himself with a clear sight of goal 12 yards out but lofted his shot over the crossbar.
Cheltenham put together their best move of the match at the start of the second half with Kayode Odejayi's strong run and Melligan's driven cross just failing to pick out a man at the far post.
However, the breakthrough came with 55 minutes played. Cheltenham won a free-kick on the edge of the Port Vale box taken by Grant McCann.
Vale cleared it and with Constantine and Sodje pressuring them, Jerry Gill passed to Victory who attempted to find his goalkeeper but under-hit the pass back and Constantine nipped in to score.
Cheltenham created a number of chances in the remainder of the half but the final shots either missed the target or found Goodlad standing strong behind them.