Cheltenham took the game to the visitors for long periods, but the quality of their passing failed to match a neat and tidy Yeovil side.
In fact, despite having the majority of chances in the match, the home side found themselves undone by some sharp thought and movement in the final third.
For all their huff and puff, Cheltenham just could not find a way back once they had gone 2-0 down.
The home side made a bright enough start to the game with Steven Gillespie receiving a return pass from Kayode Odejayi before forcing Steve Mildenhall into a full-stretch save.
David Bird then headed over the crossbar when John Melligan picked him out with a cross from the left.
Yeovil had offered little going forward in the opening stages but they grabbed a chance to take the lead with 20 minutes played.
Veteran frontman Marcus Stewart showed great awareness to collect a loose ball in the box and his chip to the far post found Wayne Gray, who rose above his marker to score with a downward header.
Stewart and Yeovil midfielder Nicky Law both went close with good chances to increase the lead, but Cheltenham hit back in the moments leading up to half-time.
Mildenhall had to be at his best again to push a drive from Bird over the bar and stretch to push aside another low shot from the lively Gillespie.
In the second half, Odejayi saw a header strike the bar and both Odejayi and Keith Lowe had efforts cleared off the line.
Yeovil, however, made the game virtually safe with 63 minutes played.
Chris Cohen found Arron Davies with a beautiful diagonal pass and the wideman motored forward before crossing low for Gray to finish from close range.
Cheltenham fought back as best they could and a Shane Duff header was cleared off the line before John Finnigan drove in a consolation goal during stoppage time.