The home side were on a high after clinching their place in the European Challenge Cup quarter-finals, and they kept up the momentum to snuff out the Blues.
Glasgow were the more potent side during the jittery opening exchanges and they broke the deadlock with a superb Colin Gregor penalty.
They pinned back the Blues in their own 22 zone with a series of well-controlled phases, forcing the defence to sneak offside.
Gregor's kick was from wide on the left, but he made it look simple. His glee turned to gloom shortly afterwards, however, when he pushed an easier effort past the near post.
The reprieve sparked Cardiff into life and they tested the home markers with several raids, but they could not turn pressure into precious points. And their frustration was underlined as Nick Macleod was wildly off target with a drop-goal bid from close range.
Having survived the storm, the Warriors came back into the game in the build-up to the interval, but they were unable to add to their account.
They came out all guns blazing after the restart to create an excellent try for hooker Fergus Thomson.
Centre Scott Barrow inflicted the initial damage with a dash through a midfield gap, with Thomson perfectly positioned to take the pop-pass and finish in style. Gregor added the tricky conversion.
The Blues clawed back three points with a Ben Blair penalty when Thomson was guilty of handling in a ruck.
But they were dealt a blow when substitute Mark Lewis was sin-binned just a minute after coming off the bench and it took Glasgow only a matter of seconds to make their numerical advantage count.
Instead of going for goal, Gregor set up a line-out in the corner. Canadian prop Kevin Tkachuk caught the markers off guard by peeling away from the maul to cruise over.
Sam Pinder almost wriggled in for another touchdown, but the ball slipped from his grasp at the last moment.
However, the replacement scrum-half made amends five minutes later, Gregor converting to make sure of the win.
The scorers:
For Glasgow:
Tries: Thomson, Tkachuk, Pinder
Cons: Gregor
Pens: Gregor
Cardiff Blues:
Pens: Blair
Yellow card: Lewis (Cardiff Blues, 61 min)
The teams:
Glasgow: 15 Rory Lamont, 14 Colin Shaw, 13 Hefin O'Hare, 12 Scott Barrow, 11 Thom Evans, 10 Colin Gregor, 9 Graeme Beveridge (c), 8 Jon Petrie, 7 John Barclay, 6 Steve Swindall, 5 Dan Turner, 4 Andy Newman, 3 Justin Va'a, 2 Fergus Thomson, 1 Kevin Tkachuk
Replacements: 16 Donnie Macfadyen, 17 Andrew Wilson, 18 James Eddie, 19 Moray Low, 20 Eric Milligan, 21 Sam Pinder, 22 Sean Marsden
Cardiff Blues: 15 Ben Blair, 14 Tom James, 13 Marc Stcherbina, 12 Nick Macloed, 11 Mosese Luveitasau, 10 Nick Robinson, 9 Ed Fairhurst, 8 Xavier Rush (c), 7 Rhys Shellard, 6 Ben White, 5 Robert Sidoli, 4 Deiniol Jones, 3 Gary Powell, 2 Gareth Williams, 1 Taufaao Filise
Replacements: 16 Scott Roberts, 17 Duane Goodfield, 18 Bradley Davies, 19 Mark Lewis, 20 Wayne Evans, 21 Dai Flannigan, 22 Dafydd Hewitt
Referee: George Clancy (Ireland)
Touch judges: Graeme Hannah (Scotland), John Ferns (Scotland)
Assessor: Neil Neil
Television match offical: Jonathan Gemmell