An opportunistic score from centre Gavin Evans stretched the lead before a try from Ollie Lindsay-Hague on the stroke of half-time reignited visiting hopes.
A brilliantly taken team try was finished off by Dan Fish at the start of the second half before Tom Williams raced in as Blues wrapped up a try bonus point in 48 minutes.
The icing on the cake came in the final minutes when a powerful pack surge saw Marc Breeze crash over to spark delighted home celebrations.
Blues started brightly from the opening minute and an early attack down the left wing saw man-of-the-match Fish kick ahead but the covering of Ollie Lindsay-Hague stopped the home wing from touching down.
The home, though, were dealt a blow as early as the fourth minute when Gareth Davies was replaced by Simon Humberstone, who started in the Quins Academy and signed new terms this week.
A series of knock-ons in the drizzle saw both teams fail to build up any momentum, although Blues showed plenty of defensive style to force mistakes from the Londoners.
Maurie Fa'asavalu looked to give Quins go forward with a barreling run down the left, but once more solid home defence forced the penalty as the visitors were guilty of holding on.
Some slick handling from Blues looked to make space tight to the touchline. However, as Fish looked to blaze away the play was brought back by referee Matthew Carley for a forward pass.
Quins started to try and open up with fly half Ben Botica at the heart of every attacking move as he looked for the short inside pass to unlock the home rearguard.
The visitors were awarded a penalty, after Blues appeared harshly penalised for a push as they went after a loose ball in midfield. And another penalty, just moments later, saw Botica kick into the corner and look to apply huge pressure.
The penalty count continued to rise in the home 22 but Blues were showing admirably resolve as they repelled a series of pick and goes before Quins were held up over the line by the sheer number of home bodies under the drive.
Back row Tom Guest, on his 200th appearance for Quins, then looked to celebrate in style as he burrowed for the line, only to lose the ball forward under pressure as he went for the whitewash.
James Down and Tom Davies combined to drive back Darryl Marfo before the game really opened up as both teams threw the ball around with real endeavour during a breathless two minute spell of free-flowing attacking rugby.
Ollie Lindsay-Hague produced a brilliant kick in behind and picked up to release Sam Stuart. The game then swung the other way as Lewis Jones drilled a low kick in behind and Richard Smith won the foot race but his footballing skills failed to hack the ball up field.
The first try of the night came just before the half hour mark as Lewis Jones spotted a gap at the back of a home scrum and peeled off down the blindside to open up Quins. When the ball was worked through the hands it found Macauley Cook who rolled up close before Paulo crashed in. Humberstone added the tough extras from out wide for a 7-0 lead.
Quins were the masters of their own downfall on 35 minutes as they looked play from deep after the ball shot out the side of a ruck. The visitors failed to gather and it was Evans who picked up and darted over unopposed with Humberstone's extras extending the lead.
The visitors looked to respond with Botica and Jordan Turner-Hall proving evasive before a penalty saw Quins this time abandon the kicking to the corner strategy and this time go for the posts. Botica, though, pushed his effort to the left of the posts.
The visitors finally crossed the whitewash as they broke tackles down the middle before a floated pass evaded Smith's grasp and picked out Lindsay-Hague to touch down in the corner to cut the lead at the break to 14-5.
Blues started the second half on the attack with neat kicks from Tom William and Fish forcing Quins to play from deep inside their own 22.
A quite brilliant score from Blues had the home crowd on its feet as sweet handling and superb running lines to the left wing saw Evans break into clear air before sending Fish over for a third try.
Back came Quins as Botica broke clear and the visitors looked to force a way over. But one over ambitious pass too many saw Owen Williams pick the intercept and race down field.
He was hauled down by Lindsay-Hague, but the supporting Blues runners quickly recycled the ball and fed Tom Williams to slide over to a huge ovation.
Lewis Jones was next to make a break clear as Blues continued to look to play before new signing Isaia Tuifua made his entrance just before the hour to a big Arms Park cheer.
Tuifua and Paulo hunted in a pack to rock scrum half Stuart back on his heels while Ellis Jenkins stripped the ball in the tackle and raced off as Blues continued to play with real energy.
A yellow card to Sam Hobbs gave Quins the numerical advantage in the closing stages, but the hosts refused to buckle under pressure.
More slick running saw Fish scamper down the left wing and his kick ahead was almost picked up by Smith, but he knocked-on and the move halted as try number five threatened.
But the try did arrive two minutes from time after a series of drives saw the pack combine and Breeze crash over to a thundering ovation.
29m Paulo t Humberstone c 7-0
35m Evans t Humberstone c 14-0
40m Lindsay-Hague t 14-5
43m Fish t Humberstone c 21-5
48m Williams t Humberstone c 28-5
78m Breeze t Humberstone c 35-5
Cardiff Blues: 15 Tom Williams (T Davies 67 (T Williams 77), 14 Richard Smith, 13 Owen Williams (Tuifua 55), 12 Gavin Evans, 11 Dan Fish, 10 Gareth Davies (Humberstone 4), 9 Lewis Jones (L Williams 60); 1 Tom Davies (Hobbs 63), 2 Rhys Williams (Breeze 63), 3 Benoit Bourrust (Andrews 27), 4 James Down, 5 Filo Paulo (Dicomidis 77), 6 Macauley Cook (Copeland 72), 7 Ellis Jenkins, 8 Luke Hamilton.
Replacements: 16 Marc Breeze, 17 Sam Hobbs, 18 Scott Andrews, 19 Chris Dicomidis, 20 Robin Copeland, 21 Lloyd Williams, 22 Simon Humberstone, 23 Isaia Tuifua