Jamie Robinson, linked with a move to Toulon in France, crossed in either half to add to early first-half strikes from Tom James and Dafydd Hewitt.
The Blues were rampant in the opening period and took a deserve 21-6 interval lead but the visitors rallied in a spirited second half effort through tries from Ruaridth Jackson, Bernardo Stortoni and Colin Shaw.
Dai Young’s men had won just three of their 10 league matches but faced little trouble in the cup competitions with nine wins from nine this season.
The capital region returned to competitive action for the first time in nearly a month following their impressive exploits in the Heineken Cup.
The Blues were without several internationals but welcomed back Wales trio John Yapp, Bradley Davies and Robin Sowden-Taylor for the visit of Glasgow.
But it was Dan Parks who booted Glasgow into a fifth minute lead before the hosts hit back within 60 seconds.
Xavier Rush, making his first start of the season, provided the go-forward and quick ball allowed Ben Blair to supply James for the opening try.
It was wing James’ first appearance since his sending off for a head butt against Gloucester in the Heineken Cup but he made amends with a clinical finish in the left corner.
Blair fired home the conversion before the Blues upped the pressure.
Hewitt, enjoying a rare start in the absence of midfield pair Jamie Roberts and Tom Shanklin, danced his way under the posts from Ceri Sweeney’s pass in the 12th minute.
The Blues were rampant and they made it 21 points in as many minutes when Robinson added his first and the third try.
The centre strolled under the posts to finish an excellent flowing move involving Rush, Sweeney and Blair before the full-back converted.
Parks added a second penalty to stem the pressure as the Blues took a commanding 21-6 interval lead.
Glasgow were thrown a lifeline two minutes after the break when scrum-half Jason Spice fumbled Parks’ deep kick through in front of the posts and Hefin O’Hare fed Ruaridth Jackson who coasted home with ease.
Parks converted and the lead was cut to a nervy eight points. Blair maintained his 100 per cent success rate with his fourth kick but turned from hero to zero within a minute when the Kiwi dropped the ball under his own posts.
Glasgow full-back Bernardo Stortoni pounced and Parks’ conversion brought the match to life – and within a score.
But Blair held his nerve and displayed ice-cool composure with the boot with his second penalty on 50 minutes.
Blair then missed his first kick of the night before the Blues secured the bonus-point on the hour mark.
Gareth Thomas’ long pass found Blair on the overlap and his inside pass allowed Robinson to touch down in the left corner.
But this try fest ended in style when Glasgow grabbed a consolation in added time through left wing Shaw.
