A lacklustre game burst into life with 54 minutes gone when Chris Turner received the ball from John Miles and hammered it on off the post for his first ever league goal.
Michael Symes hit the upright for Stanley a minute later before the striker was tackled by makeshift defender Sam Cox in the area and the referee pointed to the spot.
Phil Edwards beat keeper Scott Brown with the resulting penalty and Bobby Grant added a third three minutes later when he got on the end of Symes' flick to sidefoot home.
Grant then chipped home superbly from the edge of the area for the fourth in the 68th minute to take his tally to seven goals for the season.
Injury-hit Cheltenham suffered further woe with defender Sam Ridley getting injured in the warm-up before they lost captain Michael Townsend after half hour of the game with a back strain.
It could have been worse for them with Brown denying Symes, Miles firing wide and Grant just missing out on a hat-trick as Accrington ran riot after the break.