The odds were already stacked against an injury-hit Blues side, who were up against the Conference A leaders, who remain unbeaten in the competition.
They made the perfect start at a bitterly cold Scotstoun Stadium with Jarrod Evans slotting a penalty inside a minute and Macauley Cook crossing for a fine try.
A Sam Johnson try brought Glasgow back into the game and Danny Wilson’s men were more than in the encounter when Filise was perhaps harshly given his marching orders by referee Nigel Owens.
Despite their numerical disadvantage the Blues fought with aplomb, particularly when reduced to 13-men, but it was not enough to beat the rampant Warriors.
Evans kept the scoreboard ticking but the hosts crossed for four more tries thanks to Alex Dunbar in the first-half and Rhuaridh Jackson and Samu Vunisa crossed following the break.
The Blues remained just a score adrift of the hosts until that point but Leonardo Sarto and Niko Matuwalu crossed in the final two minutes to rub salt into the wounds.
It took the Blues just 22 seconds to earn the first opportunity for points as Glasgow were penalised soon after kick-off with Jarrod Evans slotting the simple penalty.
The Scots very nearly responded instantly as they created a bust through midfield after the Blues cleared the restart but the visitors hung on.
Glasgow went through a number of phases and pulled Cardiff Blues from left to right but were then penalised for going off their feet at the breakdown.
That enabled the Blues to clear their lines and they were soon them on the front foot as Garyn Smith and Blaine Scully combined on the right following an overlap.
They remained in the ascent and following a handful of phases there was space on the left. Evans found Willis Halaholo in space with a cut out pass and after hitting the outside he floated the try scoring ball to Cook in the corner.
Evans nailed the difficult touchline conversion to give his side a 10-0 lead after just seven minutes.
Dave Rennie’s side responded with venom and piled the pressure on the Blues. They dominated both territory and possession as the Blues clung on.
They kicked several penalties to the corner but on each occasion they were driven back by the fired up Cardiff Blues.
However shortly after the quarter mark the home side stuck. Peter Horne spotted the Cardiff defence narrow and dinked a cross-kick to the corner. Sam Johnson collected at full pace and bumped Tomos Williams off to score.
Horne added the extras before Evans responded with a penalty to make it 13-7. Glasgow continued to attack and despite the Blues holding up well, they were dealt a colossal blow just before the half hour mark.
Cook had lined up George Turner in the tackle and as the Glasgow hooker fell to the right he was caught by Filise, who was already committed.
Owens initially appeared to rule it was an accidental collision but after intervention from the TMO and several replays the veteran tight-head was harshly sent off.
The decision to dismiss Filise altered the entire dynamic of the encounter and while the Blues responded well Glasgow slowly took a stranglehold.
They soon manufactured a score as Horne fired a long pass to Callum Gibbins, who although brought to a halt managed to find Dunbar in support with a fine offload as he was bundled into touch.
The Scotland international appeared to bump into his own player in the process but Owens instantly awarded the score and Horne booted his side into the lead for the first time with the touch line conversion.
Despite their numerical disadvantage the Blues started the second-half well and earned a penalty, which Evans nailed to regain the lead.
But they were up against it against unbeaten Glasgow, who piled the pressure on Wilson’s side at every opportunity.
Wales’ Capital Region fought every step of the way as Glasgow kicked penalties to the corner and opted for scrums and they appeared to be hanging on.
However, they were dealt another blow when Olly Robinson was harshly sent to the sin-bin and the home side continued to turn the screw.
The Blues defied all the odds as they clung on but they eventually ran out of numbers as Horne put Rhuaridh Jackson away with a long-pass from close range before converting.
To their credit Cardiff Blues remained in the contest and were a just a score away from the hosts going into the final 15 minutes.
But they ran out of steam and Vunisa crossed for a close-range try with 10 minutes to spare before Sarto and Matuwalu compounded the Blues’ woes at the death.