The Warriors are still four points behind Saracens, who they face next Saturday to decide who tops Pool Five.

They led 28-10 after prop Oli Kebble bounced over on the hour, adding to tries from Grant Stewart, Scott Cummings and Chris Fusaro.

But tries from Josh Navidi and Owen Lane for Blues ensured a nervy finish before George Horne's score sealed it.

Glasgow may yet need at least a point at Saracens, who have already secured a last-eight spot after a 28-10 win in Lyon to guarantee at least a best runners-up spot, but will progress if Edinburgh beat Montpellier on Friday in Pool Five.

The Warriors also have injury concerns over back-rowers Matt Fagerson and Callum Gibbins, who were both forced off inside the first 10 minutes.

Glasgow's maul milks points

The home team had the benefit of a strong and chilling wind in the opening half, but they toiled for the most part. Glasgow had lost three in a row coming into this and they played like a side that was searching for confidence and rhythm. They created good field position after good field position but got undone by decent Blues defence and, mostly, by their own lack of accuracy and impatience.

Things changed slowly. Glasgow's maul had threatened to reap dividends early on and they milked it as the game went on. A line-out rumble early in the second quarter saw Stewart crash over for the opening score. Brandon Thomson - in for Adam Hastings at 10 - popped over the conversion to ease the tension in Scotstoun.

They got their second a few minutes later when Tommy Seymour broke the line, found Tim Swinson in support and together they took Glasgow deep into Cardiff territory. The visitors only got out of there after Ali Price played in Scott Cummings for a score that brought it to 14-0 after Thomson's conversion.

Cardiff had little to play for but some of what they did was impressive and clinical. When Lane and Dan Fish combined up the right wing they were far too slick for Glasgow, Lane gathering the chip ahead to make it 14-5.

The response came early in the new half and, again, it was the Glasgow maul that did the damage. Cardiff were a little fortunate not to have a man binned in the preamble, but they were punished on the scoreboard at any rate, Fusaro getting on the end of it.

Blues expose Warriors defence

Three tries down and one more to go for their bonus point. Another one came before the hour but it went Cardiff's way, the visitors doing Glasgow in the outside channel again. Lane put the splendid Harri Millard in at the corner. As good as the try was, the home team would have berated itself for the softness of their defence.

That would be a recurring theme for Dave Rennie's team. Cardiff continually exposed them and frightened the life out of them. When Kebble blasted over for the precious fourth try, that looked to be that. The prop took an illegal shoulder from Rhys Carre and still managed to get over the line. Carre was somehow allowed to stay on the field when he should have walked, but that was the end of Kebble's day.

The conversion gave Glasgow a 28-10 lead and while they'd stuttered their way through, the feeling was that they'd done enough to put Cardiff to sleep. They hadn't. Lousy Glasgow defence and sharp finishing from Navidi - Millard was involved again - and then another try for Lane soon after set up a fractious end-game.

With the conversion of their own fourth try, Cardiff had closed the gap to just four points. The spectre of a calamitous and tournament-ending defeat suddenly appeared in front of their eyes, but, to their credit, Glasgow went again.

They dominated the ball in the closing minutes. Three minutes from time, replacement Horne darted away from the back of a scrum close to the Blues' 5m line, shrugged off his man and skipped over for the decisive blow that ensured that Glasgow's quarter-final hopes remain very much alive.

Glasgow Warriors: S Hogg, T Seymour, N Grigg, S Johnson, DTH van der Merwe; B Thomson, A Price; O Kebble, G Stewart, D Rae, R Harley, S Cummings, R Wilson, C Gibbins, M Fagerson.

Replacements: K Bryce, A Allan (for Kebble, 62), P Du Plessis (for Rae, 70), T Swinson (for Fagerson, 7), C Fusaro (for Gibbins, 9), G Horne (for Price, 66), A Hastings, L Jones.

Cardiff Blues: D Fish; O Lane, H Millard, W Halaholo, T James; S Shingler, L Williams; B Thyer, M Rees (capt), D Lewis, G Earle, R Thornton, S Lewis-Hughes, J Navidi, S Davies.

Replacements: E Lewis (for Rees, 41), R Carre (for Thyer, 56), S Andrews (for Lewis, 50), M Cook (for Earle, 61), N Williams (for Lewis-Hughes, 50), T Williams (for L Williams, 56), J Evans (for Shingler, 50), A Summerhill (for James, 69).

Referee: JP Doyle (England)