Wales’ Capital Region led 20-14 at half-time thanks to tries from Alex Cuthbert and Rey Lee-Lo but the Warriors fought back.
A nail-biting second-half ensued at a packed BT Sport Cardiff Arms Park and Ali Price set up a tense finale.
Cardiff Blues defended with vigour and with two minutes to go Steve Shingler booted his team out of reach as they made it three from three in the Championship
The home side did not take long to get into the swing of things in front of a 8,024 crowd with Lee-Lo and Cory Allen combining to good effect. That paved the way for Gareth Anscombe to open the scoring on two minutes with a simple penalty.
They controlled the early territory and possession and turned down a shot at goal on nine minutes. Instead Anscombe dinked the ball into the corner but they were forced back by some strong Scottish defence.
The Blues went through a succession of phases before being awarded another penalty which Anscombe duly slotted.
They were presented with a further opportunity after Glasgow failed to deal with the kick-off and Lee-Lo hacked through.
Rory Clegg cleaned up but was forced over his own try-line to concede a scrum on the five metre line.
The set-piece presented the perfect attacking opportunity and Lee-Lo cut inside on a short ball from Anscombe but lost possession with the try-line seemingly at his mercy.
A sensational counter-attack by Matthew Morgan, making his first competitive appearance for the region, sliced the Glasgow defence apart and he found Tom James with a beautifully weighted miss pass.
The wing chipped ahead but did not receive a favourable bounce and the Scots took the ball over the whitewash for a second five-metre scrum.
Wilson’s men hammered away at the Glasgow defence and following a succession of phases Cuthbert sliced through for the opening try.
Anscombe added the extras to open up a 13-0 lead after 25 minutes but Glasgow did not take long to hit-back with Stuart Hogg scoring following their first real venture into the Cardiff Blues half.
They almost added a quick-fire second after working an overlap on the left once again but Ryan Wilson was unable to hang onto a long ball.
However they remained camped in Cardiff Blues territory and raised the intensity with a number of short balls around the fringes.
And it finally paid dividends when Peter Horne was not held in the tackle and he got up to crash over with Clegg converting.
But Wales’ Capital Region finished with a rally and they claimed a second try in injury time with Josh Navidi making yards down the right before sending Lee-Lo over the whitewash.
Anscombe added the extras superbly from the touchline to bring the scores to 20-14 at half-time.
The Blues made a fine start to the second-half with James, who was named man-of-the-match, demonstrating his pace and power once more as he broke through.
He was hauled down short but possession was maintained and Glasgow were at sixes and sevens, however James was penalised for holding on at the breakdown.
And just like in the first-half, having soaked up the pressure the Warriors hit-back and following some strong carries Ali Price bounced out of a thunderous collision to tumble over.
The try reduced Cardiff Blues’ lead to a single point and Clegg hit the post with the straightforward conversion.
But the Blues burst into life following the restart with James, Matthew Morgan and Lee-Lo particularly prominent.
They caused Glasgow all manner of problems but were unable to turn pressure into points as they were frustrated at the breakdown.
Again in this full throttle encounter, Glasgow powered back but Cardiff Blues demonstrated remarkable grit and determination to hold them at bay with some ferocious defence.
The encounter remained on a knife-edge as it entered the final 10 minutes but Shingler showed nerves of steel to slot a penalty and the Blues closed the game out.