But the real beneficiaries were Pool Three leaders Saracens, who are four points clear of their rivals heading into December home and away fixtures against the Blues.
Glasgow, beaten at home by Saracens last weekend, did not look back after fly-half Adam Hastings and wing DTH van der Merwe scored tries in the first five minutes.
Hastings also added a conversion and penalty before half-time, and when scrum-half Ali Price rounded off a crisp move early in the second period, the only serious debate was whether or not Glasgow would claim a five-point maximum.
Glasgow got there when lock Jonny Gray added a fourth try 12 minutes from time - again converted by Hastings - and there was no doubting their supremacy over a Blues side that fell way short of repeating last Sunday’s performance when they beat Lyon in France.
Wing Aled Summerhill claimed two consolation tries for the Blues, with Gareth Anscombe adding a conversion, but they were also chasing a game that, in truth, was beyond reach following Glasgow’s early onslaught.
The Blues knew another victory after success in Lyon would keep the pressure on Saracens, but they made a nightmare start.
Glasgow stung them with a try after just 93 seconds, stretching the Blues defence right and left, helped by outstanding work from number eight Matt Fagerson, before Hastings sliced through on an angle to touch down.
But if alarm bells were ringing in the home ranks, they took little notice as Glasgow cut them open just three minutes later when hooker Fraser Brown made initial headway, centre Huw Jones took the move on at pace and Van der Merwe finished impressively.
Hastings’ conversion took the visitors 12 points clear, and although the Blues then enjoyed a period of sustained pressure, they could find no way through a well-marshalled Glasgow defence.
And that resilient work reaped its reward after 25 minutes when Glasgow moved into the Blues half, gained a penalty and Hastings bisected the posts from 40 metres for a 15-point advantage.
The Blues finished an error-strewn opening 40 minutes by attacking strongly, driven by scrum-half Tomos Williams, but they still could not find a way through and Glasgow trooped off with a 15-0 interval lead.
Any hope the Blues had of putting themselves back in contention effectively disappeared within five minutes of the restart as Van dew Merwe surged through their defence and sent a supporting Price over unopposed from 30 metres out.
It was simple but devastatingly effective from the Warriors, and Hastings’ conversion put Glasgow one more try away from a bonus point and left the Blues with a mountain to climb.
The home side had to score next and they duly delivered as fly-half Jarrod Evans’ clever kick into space was gathered by Summerhill, who finished easily to provide a glimmer of hope.
But Glasgow were not to be denied in pursuit of a fourth try, and it came 12 minutes from time after Hastings launched a thrilling counter-attack from deep inside his own 22, and the move was finished off by Gray.
Hastings converted, putting the visitors out of sight and leaving their opponents plunging from the high of seven days ago to the low of a comprehensive home defeat, despite Summerhill’s second try two minutes from time.