The home side looked on course for a convincing win as they opened up a 10-point lead by half-time but in the end they had to thank the inaccuracy of the Blues’ kickers for their eventual triumph.
Glasgow coach Hugh Campbell was forced to make a late back-row reshuffle when flanker Andy Wilson pulled out with flu. Skipper Jon Petrie switched to the open-side to allow Paul Dearlove to fill the number eight berth, while John Beattie made his return from injury on the bench.
Glasgow had the better of the opening exchanges and opened the scoring with a simple Calvin Howarth penalty.
The Welshmen hit back positively and they levelled the contest midway through the half thanks to an opportunist drop-goal from Nick Robinson. He had an opportunity to snatch the lead shortly after, but his long range attempt was wide.
Howarth soon had the home fans on their feet again when he booted his side back in front and it was not long before they extended that advantage with a superb try from international wing Sean Lamont.
He left three markers in his wake while hurtling 50 metres – then he dived over in delight after grabbing the return pass from Howarth, who added the conversion.
The Blues bounced back after the break with another score from Robinson, but agonisingly for the visitors he missed two further subsequent chances.
A try from lock Craig Quinnell gave Cardiff fresh impetus but the wind was taken from their sails when lock Robert Sidoli was yellow-carded for killing ruck-ball. Parks stepped up and slotted the penalty from 40 metres.
He added another to kill off the Blues’ hopes, but they snatched a consolation bonus point with Nick MacLeod’s stoppage time penalty.
Final score: Glasgow 19 (try, conv, 4 pens), Cardiff Blues 14 (try, 2 pens, dg)