The visitors withstood heavy first-half pressure at Plainmoor before goals from Jermaine McGlashan and Marlon Pack confirmed a 4-1 aggregate semi-final victory.
Trailing 2-0 from the first leg, Torquay came flying out of the blocks and Town goalkeeper Scott Brown was forced into a series of impressive saves within the opening half hour.
But Martin Ling’s men ran out of steam after the interval and winger McGlashan, who opened the scoring at the Abbey Business Stadium on Sunday, effectively settled the tie with a quarter of an hour remaining.
Torquay substitute Taiwo Atieno levelled matters on the night before Robins midfielder Pack rifled home a magnificent 87th minute free-kick from 30 yards.
Mark Yates’ men travel to Wembley a week on Sunday to face a Crewe side unbeaten in their last 18 outings.
McGlashan was narrowly off target with a rasping 30-yard drive in the early stages before his side were forced to withstand a first-half onslaught.
Brown was the outstanding performer of the opening 45 minutes, and he got his night’s work under way by tipping a Eunan O’Kane effort over following some deft footwork from the Torquay midfielder.
The Gulls headed into the contest without top scorer Rene Howe due to a hamstring injury, but they were not short on attacking threat, ably demonstrated when Ryan Jarvis burst into the box and forced Brown to push behind with a superb low block.
From the resulting corner, Cheltenham defender Keith Lowe fortuitously cleared via the post as he looked to hack clear from his own goalmouth and Brian Saah fired the loose ball wide.
Brown’s best moment came courtesy of another low stop in the 27th minute when Mark Ellis’ first-time shot from Stevens’ shot emerged cleanly from a crowd of bodies.
Cheltenham striker James Spencer might have done better when he fired straight at Torquay keeper Robert Olejnik after the half hour, but it was at least an indication that Yates’ men had weathered the storm.
There was drama a minute before the interval as Torquay full-back Kevin Nicholson’s sweetly struck free-kick rattled the crossbar with Brown rooted to the spot.
The visitors immediately sprung up the other end and Olejnik stood firm to deny Kaid Mohamed.
Cheltenham began the second half with greater purpose and Olejnik gathered at the second attempt when McGlashan looked to clip home from an acute angle at the end of a mazy run.
O’Kane’s 54th minute header looped up off Robins defender Alan Bennett to force Brown into another superb save, but it soon became clear that Torquay’s early attacking verve had deserted them.
Mohamed hit a swerving shot over after a mazy run down the Torquay left by Robins full-back Sido Jombati before the decisive moment arrived in the 74th minute.
Mohamed was allowed to ease infield after collecting Ben Burgess’ pass and he played in McGlashan, who stabbed home via Olejnik’s boot and the inside of the far post.
Atieno reduced the aggregate arrears when he was left unmarked to glance in a near-post header from O’Kane’s 85th minute corner.
However, Pack applied the gloss in memorable fashion when he found the top corner after Saah fouled Jeff Goulding.