The Robins' victory gave their play-off hopes a massive boost, but it also drove a large nail into the Gulls' relegation coffin.
Yet for an hour Torquay, under new manager Ian Atkins, looked anything but no-hopers.
Visibly lifted by Atkins and with on-loan striker Lee Thorpe a constant threat up front, the Devon side forced Cheltenham back.
It was no surprise when they took the lead in the 26th minute. Thorpe chased a long ball down the middle, beat off a challenge, touched the ball over goalkeeper Shane Higgs, who had charged off his line, and rolled it into the empty net from 16 yards.
A moment later winger Martin Phillips headed just over the bar after good work by Thorpe and recalled striker Alan Connell.
Early in the second, there was little hint of what was to come, with Connell heading wide at the far-post from a Phillips cross from the right.
But it was a bad miss by Kayode Odejayi, who failed to make contact when he seemed certain to score from a Grant McCann free-kick, that sounded the alarm-bells for Torquay.
Minutes later, on the hour, Town full-back Jerry Gill crossed from the right and Damian Spencer, back in the Cheltenham attack, buried a far-post header from point-blank range. It was Spencer's first league goal since August.
Higgs pulled off one brilliant save from a Connell volley, but in the 70th minute Cheltenham struck again.
Punishing a mistake by left-back Stephen Reed, JJ Melligan hit a long ball for Odejayi to chase and, with Torquay 'keeper Andy Marriott off his line, Odejayi coolly lobbed his 12th goal of the season from 22 yards.
Atkins threw on three forwards in a desperate attempt to salvage something from the wreckage in the closing stages, but Cheltenham's defence stood firm.