Blues more than held their own for the opening 25 minutes at Scotstoun Stadium before indiscipline repeatedly cost them and the home side hit top gear and wrapped up the bonus point by the break.
A stunning six-minute blitz saw Horne (2) and Dougie Hall go over as the table toppers roared ahead.
Horne then grabbed his hat-trick with the final play of the opening 40 minutes as the Warriors opened up a commanding 29-3 lead.
Adam Ashe grabbed a fifth home try before Gareth Davies and Dan Fish struck two blows for the visitors who showed plenty of second half spirit but ultimately left empty-handed after the second quarter display.
Cardiff Blues had made seven changes going into the game - and three positional - as they looked to record a second away win in the league. One of those called into the starting line-up, Garyn Smith, was straight into the action as he thundered into two tackles.
The visiting defence was being tested in the opening minutes with Lou Reed, Sam Warburton and Josh Navidi all unloading big hits before Mike Cusack looked to break clear but spilled the ball in contact.
The first scrum of the game saw a penalty awarded to Glasgow and centre Horne nudged over the kick for the lead.
Gareth Anscombe twice looked to use his quick feet to make openings as he attacked the game line and quick handling skills from Blues sent Gareth Davies into space, but a lack of support runners saw the attack die out.
Anscombe slotted his first kick at goal on 15 minutes to draw the sides level while Horne missed his second chance of the night as he pushed his kick just left of the target.
Indiscipline was beginning to deny Blues any possession and territory and twice home fly half Finn Russell kicked to the corner, with only brave visiting defence holding firm.
Home tries, though, looked inevitable with the possession and when they arrived they came like buses in simply clinical fashion as Glasgow opened up in breathtaking fashion to showcase just why they are top of the PRO12.
Pressure told as the home forwards burrowed up close then they went wide at pace and, after centre Smith did well to stop wing DTH Van der Merwe with a last ditch tackle, it was hooker Hall that crashed over.
A second try in as many minutes then came for the hosts as slicing breaks from Tommy Seymour and Peter Murchie down the left opened up the field and sublime handling sent Horne over to score for a 15-3 lead.
More brilliant handling saw Glasgow claim a third try after 32 minutes to complete a stunning six-minute period with Horne the beneficiary once more, this time of a stunning offload on the floor, as he tore over for his second of the night.
Blues were now having to defend for long periods as Glasgow started to fizz the ball around at will and offload to try and stretch the defence and hunt for openings.
Lock Jarrad Hoeata was then yellow carded - for a miss-timed high tackle - and Horne completed his hat-trick as he cut through with the final play of the half as Glasgow took a menacing 29-3 lead into the changing rooms.
Blues needed to re-group and they started the second half with plenty of invention and creativity, but spilled ball lost early territory.
And at the other end more yet more powerful running saw Ashe brush off two tackles and the big Number Eight galloped under the posts.
Replacements Lewis Jones and Josh Turnbull combined to make inroads into the home half as Blues enjoyed their best spell of the game. And a quick tap penalty and flat pass from Fish sent Gareth Davies over to score.
Blues were looking to show their spirit and scored yet again as Matthew Rees broke a tackle, Navidi supported him on his left shoulder and the back row popped a pass to Fish to race over.
Fish should have had a second try minutes later after Garyn Smith juggled and flicked a pass to Warburton, but his low pass to the wing failed to find hands and the chance was lost.
A late flurry of action saw Tom Isaacs lead a breakout, but there was to be no further score and although Blues won the second half it was ultimately a stunning six-minute first half blitz from then hosts that ended the game.
Timeline:
05m Horne p 3-0
15m Anscombe p 3-3
26m Hall t Murchie c 10-3
28m Horne t 15-3
32m Horne t Horne c 22-3
40m Horne t Horne c 29-3
46m Ashe t Russell c 36-3
61m G Davies t Anscombe c 36-10
68m Fish t Anscombe c 36-17
Cardiff Blues: 15 Gareth Anscombe, 14 Alex Cuthbert, 13 Tom Isaacs, 12 Garyn Smith, 11 Dan Fish (R Smith 76), 10 Gareth Davies (Humberstone 78), 9 Tavis Knoyle (Jones 47); 1 Sam Hobbs (T Davies 32), 2 Kristian Dacey (Rees 50), 3 Adam Jones (Filise 41), 4 Jarrad Hoeata (Jenkins 64), 5 Lou Reed (Turnbull 40), 6 Macauley Cook, 7 Sam Warburton, 8 Josh Navidi
Replacements: 16 Matthew Rees, 17 Thomas Davies, 18 Taufa’ao Filise, 19 Josh Turnbull, 20 Ellis Jenkins, 21 Lewis Jones, 22 Simon Humberstone, 23 Richard Smith