The Warriors pack controlled the set-piece throughout the game at Cardiff Arms Park and the Blues were restricted to a solitary Leigh Halfpenny penalty on the stroke of half-time.
Despite losing Dougie Hall to the sin-bin in the final quarter the Warriors never looked like buckling under pressure - the win perfect preparation for next weekend's Heineken Cup clash with Northampton Saints.
Proceedings were cagey in the opening quarter as both sides struggled with handling errors as they attempted to spread the play wide.
After a scoreless opening quarter Cardiff's indiscipline handed the initiative to Warriors, Horne opening up a nine-point lead after repeated infringements at the breakdown.
After a delay on the half-hour mark following a collision between Warriors skipper Al Kellock and Campese Ma'afu Horne added a fourth penalty to stretch the lead to 12.
The visitors were playing the better rugby and dominating at the set-piece but a series of handling errors in the Blues 22 prevented them from crossing the line.
With the clock ticking down to half-time Leigh Halfpenny got the Blues off the mark with a simple penalty in front of the posts to make the score 3-12 at the break.
Glasgow were not deterred by the Blues late score and came storming out of the blocks after the interval, scrum-half Henry Pyrgos sniping well as the visitors looked to exploit gaps in Cardiff's backline.
Four minutes into the half Horne held his nerve to score from out wide after replacement Taufa'ao Filise was penalised for handling in the ruck, extending the lead to 15-3.
While Horne had a 100 per cent record Halfpenny missed his next chance, dragging a 50th-minute penalty wide of the posts from halfway after a rare Warriors infringement at the breakdown.
As the match approached the hour mark the Warriors continued to turn the screw, Horne extending the lead to 15 points with his sixth successful penalty of the evening.
While Horne was on form in front of the sticks Stuart Hogg was soon the hero at the other end, the replacement full-back getting across to knock the ball out of Halpenny's hands on the line after a good passage of play by the hosts.
Despite being on the back foot for most of the match the Blues were now in the ascendancy but Glasgow refused to buckle in the face of heavy pressure.
With 15 minutes to play Cardiff were handed a lifeline as Warriors hooker Hall was sent to the bin for cynical play at the breakdown.
But the hosts were unable to make the numerical advantage count, and could have fallen further behind on 77 minutes had Horne found target with his seventh penalty of the evening.
By the time Hall returned to proceedings the score-line was the same as when he had left the field, the Blues unable to make a breakthrough as the Warriors defence remained firm to record a comprehensive win.
|Cardiff Blues Score Card|
|Glasgow Warriors Score Card|