Glasgow came into the game fresh from a bonus-point success over league leaders Ulster, but well-aware of the threat of European champions Leinster.
Gregor Townsend's side had won six straight RaboDirect PRO12 to put themselves in an ideal position to push for a home semi-final, but knew they could not afford to slip up at home to the Blues.
Phil Davies' team slumped to a 26-22 home defeat to Connacht on their last outing, but enjoyed success in Scotland a week earlier in Edinburgh.
But it was the home side who should have taken the early lead with a penalty from Duncan Weir - back from international duty - missing a third-minute penalty from halfway.
However the respite was only temporary for the Blues with Horne running in the first home try. The centre endured a difficult evening in the Ulster success, missing every kick he attempted, including an eminently kickable late conversion.
That appeared to have no impact on him in this encounter though, with the 23-year-old scoring a stunning solo effort to put the Warriors in front. Weir added the conversion as Glasgow led 7-0 after a quarter of an hour.
The Blues responded well, and ten minutes later they were level when openside flanker Josh Navidi, playing in the absence of Sam Warburton, went over.
Rhys Patchell slotted the conversion to level things, and he was on target again just after the half-hour with a penalty to put the Blues 10-7 up.
Weir responded immediately with a penalty of his own, but Patchell had the final say of the half as the Blues led 13-10 at the break.
Whatever Townsend said at half-time clearly worked as the Warriors came out a completely different team, giving their visitors no chance in the second 40.
It took them 15 minutes, but eventually they found a way over, and almost inevitably it was their inspirational scrum-half Nikola Matawalu who scored.
The Fijian's fourth try in five RaboDirect PRO12 matches put the home side back in front, Weir converting to make it 17-13.
Three minutes later Weir added Glasgow's third try, converting it himself to put the result beyond doubt.
And it took just four more minutes for Glasgow to secure the bonus point, Matawalu again proving the difference in a sensational recent run.
Scott Wight, who had just come on for Weir, missed the conversion and a later penalty but it made little difference for Glasgow.
|Glasgow Warriors Score Card|
|Cardiff Blues Score Card|