Warriors end Cheetahs' run
The victory takes the Warriors start to six successive wins for the season and ended the Cheetahs' three-match winning streak.
The Cheetahs dominated the set pieces, especially the scrums, where they won a number of penalties, but the contest at the breakdown was a lottery.
In the opening quarter, they threatened to run their Scottish visitors off their feet, but the Pool A leaders hung tough and scored four great tries for the bonus-point win.
It was Rob Harley's wonderful late try that ensured Glasgow' winning start continued.
Harley crashed over from Finn Russell's expert kick, the last act in a game that continued to to-and-fro from almost first minute to last in a game featuring two teams on top form.
Callum Gibbins scored his first two tries for the Warriors, while Henry Pyrgos also got his name on the scoreboard in a bonus-point win.
But it wasn't to all go the Scottish side's way as Sergeal Petersen and Rosko Specman as well as an impeccable kicking effort from kept the hosts fighting for the entire contest.
Glasgow wasted little time getting themselves on the board, winning a penalty with barely a minute on the clock from which Finn Russell expertly put his side three points ahead.
But the Cheetahs came back with a bite, pinging the ball out to the touchline from a quick penalty where fullback Petersen was on hand to crash over for the first try.
And it was the hosts who next troubled the scoreboard with a penalty, but an intense spell of Warriors pressure had them back to parity as flank Gibbins charged over for his side's first score, Russell converting to level it up at 10-all.
It looked for all money that that would be the half-time score, only for a superb length-of-the-field score leading to Specman crashing over and putting the Cheetahs seven points ahead come the interval.
But the second half saw Gibbins become the man to once again do the damage – but he had plenty to thank Ruaridh Jackson for.
The fullback intercepted on his own try line to sprint away down-field, finding Gibbins in exactly the right place at the right time for the pass and score to make the game level once more.
That was how it stayed until the 57th-minute mark but the Cheetahs poked their noses in front again, Ernst Stapelberg twice kicking penalties.
But, with just 10 minutes to go, Glasgow showed exactly why they have been impeccable this season with some lovely play through the hands, the ball eventually finding Pyrgos to dot down and put his side ahead by just one point coming towards the denouement.
But the hosts were prepared for yet another twist in the tale, with Stapelberg getting his fourth penalty to tip the scales for the last time – or so we thought.
With just two minutes to go, up stepped Russell with a beautiful chip to the corner to allow Harley to crash over for the bonus point score and yet another victory on the road for the Scots.
For the Cheetahs:
Tries: Petersen, Specman
Cons: Stapelberg 2
Pens: Stapelberg 4
For Glasgow Warriors:
Tries: Gibbins 2, Pyrgos, Harley
Cons: Russell 3
Cheetahs: 15 Sergeal Petersen, 14 Rosco Specman, 13 Francois Venter (captain), 12 William Small-Smith, 11 Makazole Mapimpi, 10 Ernst Stapelberg, 9 Tian Meyer, 8 Teboho Mohoje, 7 Henco Venter, 6 Paul Schoeman, 5 Reniel Hugo, 4 Justin Basson, 3 Tom Botha, 2 Torsten van Jaarsveld, 1 Charles Marais.
Replacements: 16 Jacques du Toit, 17 Retshegofaditswe Nche, 18 Johan Coetzee, 19 Rynier Bernardo, 20 Junior Pokomela, 21 Shaun Venter, 22 Nico Lee, 23 Luther Obi.
Glasgow Warriors: 15 Ruaridh Jackson, 14 Tommy Seymour, 13 Nick Grigg, 12 Sam Johnson, 11 Leonardo Sarto, 10 Finn Russell, 9 Ali Price, 8 Adam Ashe, 7 Callum Gibbins, 6 Ryan Wilson (captain), 5 Jonny Gray, 4 Tim Swinson, 3 Zander Fagerson, 2 Fraser Brown, 1 Jamie Bhatti.
Replacements: 16 George Turner, 17 Alex Allan, 18 D'Arcy Rae, 19 Brian Alainu'uese, 20 Rob Harley, 21 Henry Pyrgos, 22 Peter Horne, 23 Niko Matawalu.
Referee: George Clancy (Ireland)
Assistant referees: Cwengile Jadezweni, Ben Crouse (South Africa)
TMO: Shaun Veldsman