The Currie Cup champions were in fine form from the outset, scoring three first-half tries for a 24-7 lead, and they added four more after the break while limiting the visitors to two in the match for the morale-boosting win.
Experienced scrumhalf Ruan Pienaar was rock-solid in his performance, scoring a try and kicking five conversions and penalty goal for his 18 points, while Joseph Dweba (hooker) and Rhyno Smith (fullback) scored braces.
Pienaar opened up the scoring in the sixth minute after gathering the ball at the right place at the right time, and he added the conversion and a penalty goal minutes later to stretch their lead to 10-0 in the 10th minute.
They added to this 11 minutes later with Dweba dancing his way through the defence and using his raw pace to get to the line.
The Glasgow Warriors hit back with Nick Frisby (scrumhalf) touching down after two clever kicks, but this was cancelled out minutes later as Dweba scored his second try from a rolling maul, which nudged the hosts into an encouraging lead.
The visitors came out firing in the second half with Robbie Nairn (winger) scoring their second try in the 52nd minute thanks to a well-timed pop pass, but the Toyota Cheetahs bounced back minutes later with a try by Smith, who finished off a great break in the midfield.
Junior Pokomela scored his first try of the match in the 62nd minute after some great inter-passing and Smith backed this up soon after with his second try after catching a fantastic chip kick.
The Toyota Cheetahs ensured that they finished the match strongly with Sias Koen (replacement flanker) touching down from another fantastic phase of hard running and good support play, which steered them to the rewarding 48-14 victory.
Toyota Cheetahs 48 (24) – Tries: Ruan Pienaar, Joseph Dweba (2), Junior Pokomela, Rhyno Smith (2), Sias Koen. Conversions: Ruan Pienaar (5). Penalty Goal: Ruan Pienaar.
Glasgow Warriors 14 (7) - Tries: Nick Frisby, Robbie Nairn. Conversions: Brandon Thompson (2).