An aerial bombardment by international fly-half Dan Parks led to two tries, which had the 7,603 home crowd worried for a while, but the Blues’ dominance at close quarters and greater penetration behind saw them home in the end.
Even though Parks gave Glasgow an early lead with a long-range penalty, the Blues swept down field to claim three tries in 13 minutes.
Flying winger Tom James, on his first appearance since his red card at Gloucester, cut inside to take a neat Ben Blair pass and dart through despairing arms to score the first.
Inside centre Dafydd Hewitt grabbed the opportunity of a rare outing to side-step and jink his way over for the second.
And his midfield partner, Jamie Robinson, who is leaving the Arms Park in the summer to play in France for Toulon, ended a flowing move by dummying his way past Glasgow full-back Bernardo Stortoni to complete the blitz.
Blair converted all three and there were further blows for the visitors with flankers Kelly Brown and Stevie Swindall both leaving through injury.
Brown, a Scotland substitute in Paris last weekend, took a blow to the head, which must be a worry for national coach Frank Hadden.
Parks kicked a second penalty before half-time, but his side had to defend grimly to avoid conceding a bonus point before the break.
Yet it was Glasgow who claimed the first touchdown of the second period, although it was a gift from Blues scrum-half Jason Spice, who failed to hold onto Parks’ kick ahead.
Welsh winger Hefin O’Hare snaffled the loose ball and sent centre Ruaridh Jackson in for a try which Parks converted.
Another up-and-under from the fly-half caused chaos, dropping in the Blues in-goal area. Blair, under pressure, fumbled the ball and it fell invitingly for Stortoni to touch down.
Parks again added the extras and it was only a brace of Blair penalties that kept the home side in front.
The Blues gradually regained control, however, and Robinson, earlier denied by a forward pass, claimed their fourth try on the word of the TV official. Blair’s conversion extended the lead to a more comfortable 14 points.
But Glasgow were still not finished, Parks kicking another penalty and converting an injury-time touchdown by wing Colin Shaw before the final whistle brought relief to the home camp.
Cardiff Blues scorers: Tries: James, Hewitt, J. Robinson 2. Cons: Blair 4. Pens: Blair 2.
Glasgow: Tries: Jackson, Stortoni, Shaw. Cons: Parks 3. Pens: Parks 3.
CARDIFF BLUES: Blair; G Thomas, J Robinson, Hewitt, James; Sweeney, Spice; Yapp, G Williams, Filise; Davies, Tito; Molitika, Sowden-Taylor, Rush.
Replacements: Mustoe for G. Thomas (55), Rees for Spice (56), G. Powell for Filise (55), D. Jones for Tito (60).
GLASGOW: Stortoni; O’Hare, Nunez Piossek, Jackson, Shaw; Parks, McMillan; Va’a, Hall, Low; Turner, Kellock; Swindall, Brown, Beattie.
Replacements: Thomson for Hall (54), Kalman for Low (64), Palepoi for Swindall (22), Forrester for Brown (12).
Referee: Alain Rolland (Ireland).
Guinness Premiership Result: Sale 32 (Tries: Roberts, Fernandez Lobbe, Abraham, Briggs. Cons: Hodgson 3. Pens: Hodgson 2) Bristol 13 (Tries: Ward-Smith. Cons: Jarvis. Pens: Jarvis 2); Newcastle 13 (Tries: Rudd. Cons: May. Pens: May 2) Saracens 9 (Pens: Jackson 3).