High-flying Glasgow, who are now undefeated on the road in the league in seven games, had trailed going into the final ten minutes.
But tries from James Eddie and Mark Bennett left Blues to take just a losing bonus point from the encounter.
A first half try from Robin Copeland had given Blues a more than deserved 10-0 lead before a score from Lee Jones on the stroke of half-time gave Glasgow the platform to build.
Scrum half Lewis Jones scored an opportunistic try at the start of the second half, but the momentum slowly swung to Glasgow and the late double sunk the home side.
Blues made seven changes to the side that were defeated by Munster with Isaia Tuifua handed a full debut while Richard Smith, Dafydd Hewitt, Simon Humberstone, Scott Andrews, Gethin Jenkins and Sam Warburton all returned.
Tuifua was straight into the action as his big hit dislodged the ball and Richard Smith picked up as the home side went onto the attack in the opening two minutes.
The returning Warburton produced a slick behind the back pass and back row team-mate Ellis Jenkins then repeated the trick as Blues looked to open up Glasgow with some neat handling before Dan Fish saw his chip kick just run dead before he could reach the ball.
A penalty at the first scrum of the game, won by Gethin Jenkins, saw Fish kick to the corner to set up the driving maul. Glasgow duly infringed at the lineout and Humberstone drilled over the kick.
Blues were playing some neat incisive attacking rugby behind the solid scrum as Fish looked to blast away from Rory Hughes on the outside before grubber kicking in behind to force Nikola Matawalu into action.
The home set piece was working efficiently in the opening quarter with another big scrum allowing Humberstone to pump the ball clear.
Blues continued to dominate territory and possession, but spilled ball in the tackle allowed Glasgow to run from deep and threaten to expose the spaces left.
The home was dealt a blow on 19 minutes when scrum half Lloyd Williams limped off, after picking up an injury a few minutes earlier, and was replaced by Lewis Jones.
A penalty from Ruaridh Jackson slipped wide of the target a minute later. Mark Bennett then took over kicking duties on 24 minutes, after the home side strayed offside in defence, but his kick struck the right upright and bounced clear.
Irish ace Robin Copeland manufactured a brilliant turnover at the breakdown as he stripped the ball and then took a high bomb kick and raced it back as play switched from end to end at real pace.
The opening try of the game came just after the half hour as Macauley Cook broke down the wing at pace as Blues looked to expose an overlap.
The young lock threw the ball back inside, as he was bundled into touch, where Glasgow’s Jackson then flicked the ball back blind to keep it alive, but only to Humberstone who gratefully gathered and applied the final pass to Copeland to stride over for a 10-0 lead.
Blues need to keep the door shut until half-time, but were guilty of giving away a soft try in the final minute as Lee Jones skipped out of several tackles to touch down with Jackson’s conversion cutting the lead to three points at the break.
Matawalu tried to fashion a break with a cute kick in behind at the start of the second half before Copeland broke down the left and into free air, but could not find the man supporting on the wing.
Fish created something from nothing as he collected a box kick and then grubbered in behind and picked up the loose ball.
Blues swarmed forward and several forward bursts saw Warburton and Kristian Dacey burrow forward before the ball squirmed out the side of the ruck and Lewis Jones pounced over the line.
Several reviews of the score by the TMO Gareth Simmonds eventually saw the try given and Humberstone’s extras made it 17-7 to Blues.
Wing Harry Robinson was clattered as he cleared the ball from the restart by opposite number Hughes and the penalty was awarded for not using the arms in the tackle.
The visitors produced some neat hands of their own in midfield and charged down the middle until the final pass was picked off by Filo Paulo and Jones and Robinson combined to clear the danger.
The Warriors were coming strong and starting to control territory and possession as he looked for a way back into the game. They were presented with three points after Blues infringed at the breakdown and Finn Russell did the rest.
Blues were having to work exceptionally hard as Glasgow continued to monopolize the ball with the pack forcing a turnover as Warriors looked to the driving lineout for attacking joy.
A charged down kick off Gareth Davies sparked another visiting attack, and when Blues conceded the penalty the resulting kick from Russell cut the lead to four points.
Blues finally mounted an attack after relentless Scottish pressure and they won a penalty for not rolling away in the tackle as Jones went digging for the ball at the breakdown. Davies lined up the resulting kick and slotted it to make the score 20-13.
The momentum, though, continued to be with Glasgow as James Eddie showed real pace down the middle to make 40 metres before he was hauled down. A drive for the line resulted in a five-metre scrum and Warriors broke through with the try awarded to Eddie.
With the game all to play for in the final minutes it was Blues who attacked first after Fish drilled a threatening kick into the corner. However, a not straight lineout saw the opportunity lost.
Glasgow, by comparison, were ruthless two minutes from time when a scrum against the head saw Warriors attack right at pace and a looped pass picked out Mark Bennett to dot down and end home hopes.
Timeline:
07m Humberstone p 3-0
34m Copeland t Humberstone c 10-0
39m Jones t Jackson c 10-7
47m Lewis t Humberstone c 17-7
54m Russell p 17-10
65m Russell p 17-13
68m Davies p 20-13
71m Eddie t Russell c 20-20
78m Bennett t Russell c 20-27
Cardiff Blues: 15 Dan Fish, 14 Richard Smith, 13 Isaia Tuifua, 12 Dafydd Hewitt (Williams 60), 11 Harry Robinson, 10 Simon Humberstone (Davies 54), 9 Lloyd Williams (Jones 19); 1 Gethin Jenkins (Hobbs 54), 2 Kristian Dacey (Williams 68), 3 Scott Andrews (Palmer 77), 4 Macauley Cook, 5 Filo Paulo, 6 Ellis Jenkins, 7 Sam Warburton (Watts-Jones 60), 8 Robin Copeland
Replacements: 16 Rhys Williams, 17 Sam Hobbs, 18 Patrick Palmer, 19 James Down, 20 Rory Watts-Jones, 21 Lewis Jones, 22 Gareth Davies, 23 Tom Williams