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Hooker Pat MacArthur burrowed over to open the scoring, with Blaine Scully scampering down the left to strike back for the visitors before half-time.
Glasgow full-back Peter Murchie scored twice from close range after the break.
MacArthur's replacement James Malcolm drove over to secure the hosts a bonus point, before Rhun Williams raced in for a late Blues consolation.
Glasgow's win sent them above Blues' Welsh rivals Scarlets, who narrowly beat sixth-placed Ulster in a match that caused controversy on Friday.
Sitting seventh before kick-off with three defeats in their past four league outings, Blues knew they needed a win to narrow the gap on the top four.
However, they were forced onto the back foot from the off, the hosts piercing the Welsh defensive line through Tommy Seymour and Josh Strauss, before Ryan Wilson was held up over the try-line.
Warriors would not let up, and after several phases of pummelling the visitors' line, MacArthur powered over under the posts.
The Blues responded well and would have reduced the seven-point gap had Wales and Lions wing Alex Cuthbert not lost control of the ball with the whitewash within stretching distance.
The rain was now falling hard on the synthetic Scotstoun surface and the wet ball was proving increasingly difficult to retain for both sides. Glasgow were starting to exert their authority at scrum-time though, and fly-half Finn Russell kicked the home side into a 10-point lead when the Welsh pack infringed at the set-piece.
Warriors were utterly dominating territory and possession, but they were stung right at the end of the first half. Russell, who this week has been linked with a move away from Glasgow, attempted a risky cross-field kick on his own 22 metre line.
The kick was partially charged down and the loose ball was pounced on by wing Scully to touch down. Steven Shingler nailed the touch-line conversion, and the fly-half's penalty early in the second half levelled the match.
The ball was squirting out of hands all over the pitch until Glasgow concocted the move of the match to regain the initiative and the lead.
Mark Bennett slipped a cute pass to Seymour tearing into the line off his wing and through a gaping hole. He fed Alex Dunbar who, despite having two team-mates outside him, dashed for the line and was held up short.
The Scotland centre's blushes were spared when Murchie blasted over from the resultant ruck. Russell supplied the extras and Glasgow were seven clear again.
Seymour, the game's standout performer, was at it again a few minutes later, exploiting a gap around the fringes to take his team into the red zone again. When the ball was recycled Bennett once more showed silky hands to put Murchie in for his second try of the evening.
Leading 24-10 and in charge, the big question was whether Warriors could find a fourth try with a quarter of the match remaining. They let slip bonus-point opportunities against Edinburgh in the league and Racing 92 in the Champions Cup, but they were not going to leave the extra point behind here.
Substitute Malcolm was the man in possession when a rolling line-out maul was driven over the Cardiff line. 29-10 - job done.
There was time for a late consolation score for the visitors when Williams touched down, but the defeat leaves their play-off hopes in a perilous state.
Fourth-placed Glasgow now switch their attention to Europe and a Champions Cup showdown with in-form Munster next weekend.
Glasgow: Peter Murchie, Tommy Seymour, Mark Bennett, Alex Dunbar, Lee Jones, Finn Russell, Ali Price, Gordon Reid, Pat MacArthur, D'arcy Rae, Tim Swinson, Jonny Gray (capt), Josh Strauss, Simone Favaro, Ryan Wilson.
Replacements: James Malcolm, Alex Allan, Zander Fagerson, Rob Harley, Adam Ashe, Grayson Hart, Rory Clegg, Sean Lamont.
Cardiff Blues: Matthew Morgan; Alex Cuthbert, Rey Lee-Lo, Willis Halaholo, Blaine Scully; Steven Shingler, Lloyd Williams; Rhys Gill, Kristian Dacey, Anton Peikrishvili, Macauley Cook, James Down, Ellis Jenkins, Sam Warburton (capt), Josh Navidi
Replacements: Matthew Rees, Brad Thyer, Scott Andrews, Jarrad Hoeata, BJ Edwards, Tomos Williams, Nicky Robinson, Rhun Williams
A:

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Glasgow Warriors regained fourth place in the Pro12 table with a 29-15 bonus-point victory over Cardiff Blues.