The Gulls stormed into a third-minute lead as on-loan Derby striker Callum Ball latched on to a Chapell pass to put the home side ahead.
Ball's early opener was cancelled out from a 13th-minute free-kick as Keith Lowe's floated cross was headed home by target man Byron Harrison on the six-yard line.
Ball was credited with his side's second goal in first-half stoppage time as his swiped shot deflected off marker Steve Elliott and looped over Robins' keeper Scott Brown following Karl Hawley's left wing cross.
Striker Hawley extended Torquay's lead in the 49th minute when he beat Brown with a low angled shot from 10 yards after cutting inside from the left after good work down the flank from winger Jordan Chappell.
Cheltenham reduced the deficit after 65 minutes when Terry Gornell latched on to a Russell Penn through-ball to fire under United keeper Martin Rice.
Chapell made absolutely sure of the points at the death with with a left-footed strike from the left of the penalty area.