McGlashan gave Mark Yates's side the lead on 27 minutes when he converted in clinical fashion from close range before throwing over a cross for Ben Burgess to power a header into the net from 12 yards out five minutes after the break.
It was little more than the home side deserved after Cheltenham dominated large swathes of a match against a visiting side who appear to have taken their poor league form into these play-off matches.
Torquay remain without a win in their past six matches while the home side have now careered to three straight victories before the return leg at Plainmoor on Thursday night.
The visiting side carved out the first chance of the day with Rene Howe thrashing an effort over the bar from the edge of the home area on two minutes.
Despite appearing to be struggling with a hamstring strain, Howe - who was replaced late in the first period by Taiwo Atieno - played in Ryan Jarvis, whose effort was nudged wide by Scott Brown in the Cheltenham goal.
Brown missed Kevin Nicholson's corner seconds later before Lee Mansell dragged his shot wide after some bedlam in the home area.
Cheltenham's first move of serious intent saw Torquay goalkeeper Robert Olejnik fist Burgess's header over the ball from McGlashan's delivery.
McGlashan was not to be denied on 27 minutes when he raced onto a lovely defence-splitting pass by the lively Luke Summerfield to send the ball spinning beyond Olejnik.
Torquay continued to look dangerous in spells with Brown diving to nudge an Ian Morris effort wide of his post before Mansell saw an overhead kick drop wide three minutes before the break.
Jarvis blew Torquay's best chance of the match when he powered a header against the bar from Eunan O'Kane's delivery when he should have netted.
Atieno forced Brown to make saves in the final 10 minutes, but Cheltenham were hardly under duress as they saw out the closing five moments without too much fuss.