The Robins played like a team already relegated in that there appeared to be no pressure on their players, who passed the ball around with relaxed ease.
Hartlepool, on the other hand, are still weighted down by the cares of trying to stave off the drop to League Two and appeared lethargic and lacking cohesion for long periods.
Cheltenham could have taken an early lead when Hartlepool defender Ritchie Humphreys made a last-ditch tackle to deny Elvis Hammond, although the former Leicester City man was not to be denied ten minutes before the break.
Hartlepool captain Michael Nelson, who had an otherwise excellent game, handled in the box from Hammond 's shot and the striker took the penalty kick himself, sending goalkeeper Arran Lee-Barrett the wrong way.
Hartlepool looked to have scored just before half-time when Cheltenham's Andy Lindegaard headed off the line from a back header by his own player David Bird.
The Pools players protested that the ball had already crossed the line but the assistant referee kept his flag down.
Hartlepool also began the second half strongly but were unable to capitalise on their advantage.
Cheltenham goalkeeper Scott Brown made fine saves from Joel Porter, Keigan Parker and substitute David Foley, while Porter shot over the bar after displaying some sharp skills to create a chance for himself in the penalty area.
Despite those chances, Hartlepool never really convinced the crowd of only 2,945 that they could get back into it and the door was finally slammed on them a minute from time.
Lindegaard played a free-kick down the right-hand side, Josh Low turned the ball inside for teenage substitute Nicholas Bignall and the on-loan Reading youngster produced a sharp turn on the edge of the area before shooting low past Arran Lee-Barrett.