The Blues, with six successive home wins behind them in the league, showed welcome adventure from the first whistle, but slipshod handling let them down.
A burst by lively scrum-half Mike Phillips looked promising, but he ran away from the support and was happy to settle for a penalty, kicked by Blair.
The New Zealander added a second to reward steady home pressure before showing the Arms Park fans what they can expect with the first half’s only try.
A brilliant jink by young centre Tom Riley created space and his delayed pass allowed Blair, running excellent lines from full back, to side step the last defender to reach the posts, giving himself an easy conversion.
It was almost half time before Glasgow penetrated the Blues’ 22, earning a penalty which Dan Parks kicked, and the Scotland fly half slotted another after Tom Shanklin conceded 10 metres by foolishly hoofing the ball away.
Parks completed his hat-trick from the halfway line to open the second period, but just as Blues supporters were becoming twitchy their side conjured up another try.
A high kick by Nicky Robinson was claimed by Shanklin, Robinson’s long pass then found Mosese Luveitasau in midfield, and the Fijian winger raced around the whole Warriors front row to score. Blair converted.
Shanklin celebrated his return to fitness with a try from an inside pass by Robinson, Blair’s conversion putting the Blues out of sight.
But the Lions centre, who played only once all last season, soon needed treatment again on his troublesome knee, although he was able to walk from the field unaided.
Glasgow left wing Thom Evans showed his pace with two tremendous sprints down the touchline, only a last-ditch tackle by the outstanding Blair saving the Blues’ line.
The home side came close to a bonus point but Chris Czekaj knocked on in the act of touching down.
Cardiff Blues scorers: Tries: Blair, Luveitasau, Shanklin. Cons: Blair 3. Pens: Blair 2.
Glasgow: Pens: Parks 3.
CARDIFF BLUES: Blair, Luveitasau, Riley, Shanklin, Czekaj, N. Robinson, Phillips, Jenkins, Thomas, Filise, Jones, Sidoli, Morgan, M. Williams, Rush.
Replacements: Macleod for Shanklin (70), Fairhurst for Phillips (71), Yapp for Filise (76), Lewis for Rush (73).
GLASGOW: Leonelli Morey, O’Hare, Henderson, Barrow, Evans, Parks, Beveridge, Va’a, Thomson, Murray, Newman, Kellock, Wilson, Barclay, Beattie.
Replacements: Marsden for Leonelli Morey (46), Gregor for Parks (61), Pinder for Beveridge (40), Milligan for Thomson (69), Turner for
Newman (40), Forrester for Wilson (55).
Referee: A Rolland (Ireland).