The Scottish outfit secured a bonus point during the opening 40 minutes, building up a 25-point lead at the interval.
John Mulvihill's side saw two tries disallowed either side of half time, with Olly Robinson and Brad Thyer going close.
However, it was a much improved performance from the visitors after the break, with Kristian Dacey and Jarrod Evans crossing the whitewash, but the Warriors proved deadly on the counter to maintain their place at the top of Confernce A.
The newly-capped Evans got the scoreboard ticking with an early penalty, after the hosts were penalised at the breakdown.
However, Glasgow soon showed what they were capable of with ball-in-hand. Nick Grigg was released in midfield, and had Ali Price in support, who looked destined for the line. However, Tom Williams had other ideas, showing impressive pace to make a last ditch tackle on the scrum half.
Minutes later the Warriors did cross for the opening try of the game. Ruaridh Jackson managed to free his hands in the tackle to release Adam Ashe with an offload, and the number six had the space to run in unopposed.
Despite an initial positive response from John Mulvihill’s side, a pair of penalties for the hosts gave them territory to hunt a second try.
A strong driving maul gave them a platform, and a neat pop by Price to Niko Matawalu, making his 100th appearance for the club, paved way for the Fijian to run in from the 22m line. Horne again added the extras.
An Evans penalty attempt sailed wide of the left hand posts, after some fine work at the breakdown from Nick Williams, before full back Williams was once again found himself forced to deny Glasgow an almost certain try.
This time the 27-year-old intercepted Price's attempted pass inside.
A quick tap from deep did pave the way for the Warriors’ third of the half. They went through the motions out wide, and Grigg’s inside ball allowed Callum Gibbins to stretch for the whitewash.
Despite a missed penalty from Horne, the hosts managed to secure a bonus point before the interval. Grigg broke from the right hand side and had support from British and Irish Lions wing, Tommy Seymour, who made no mistakes to run in under the posts.
Cardiff Blues looked to strike back before the interval, and a series of close-range penalties saw them agonisingly close. Robinson looked over in the corner, but was judged to have been held up by the TMO.
Thyer was also denied a try shortly after the break, but moments later Dacey touched down from the base of a strong drive to give his side their first try of the evening.
Rory Hughes added a fifth for Glasgow after a period of sustained pressure, but Harri Millard and Evans proved to be threats with ball in hand, making breaks into the hosts’ 22.
The outside half made the most of the platform he created, as he showed a combination of his power and evasiveness to cross the whitewash.
The visitors had a foothold in the game during the second half, enjoying much more possession and territory, as replacements such as Lewis Jones looked dangerous at times.
However, with the away side looking to chase a potential bonus point, Matawalu intercepted from deep and had the gas to run in from his own half to seal the win.