The Blues went down 34-13 at the Cardiff City Stadium to finish the weekend in sixth place in the new RaboDirect PRO12 table.
Promising victories over Edinburgh and Treviso in the opening two rounds of action have now been followed by a trio of losses, with Ulster and Munster both matching Glasgow’s success.
The Blues went into the fixture looking to bounce back from last weekend’s narrow defeat to the reigning champions but again came out second best on home soil.
Glasgow outscored their hosts by four tries to two and were good value for their convincing win, even if they had to wait until the final minute for their bonus-point score.
The Blues endured a poor start as they conceded a try to Warriors scrum-half Colin Gregor with 13 minutes gone but the manner in which they responded suggested a positive result was still on the cards.
Kiwi centre Casey Laulala added a 23rd-minute try to Ceri Sweeney’s earlier penalty and the Blues led for the first time in the match. But it proved to be a false dawn as Glasgow took control to lead 17-8 at the break thanks to a converted try from James Eddie and a penalty from fly-half Duncan Weir.
Lewis Jones saw yellow for the Blues just before Weir’s penalty on the stroke of half-time, leaving the Blues to begin the second period with 14 men. Despite the numerical disadvantage, the Blues held firm while Jones was off the field and would have even narrowed the gap had Sweeney been successful with a penalty attempt just a minute after the interval.
But things took another turn for the worse when Jones returned to the action, with Tommy Seymour’s 52-minute score and Weir’s conversion handing the Warriors a 24-8 advantage.
The Blues bounced back again with a Michael Patterson score 10 minutes later but Sweeney failed to add the extras and Weir put the game beyond doubt with his 69th-minute penalty.
Stuart Hogg then put a gloss on the away side’s win with the 80th-minute effort that ensured the Scots left with the maximum five points.