Stand-in skipper Logan shook off the effects of an ankle injury to inspire his side – claiming two of their tries as they surged to a crucial bonus point

But the triumph was tarnished when prop Euan Murray was red-carded for illegal use of the knee.

Stand-off Calvin Howarth had got the Scots up and running with two early penalty strikes for offside.

Llanelli bounced back briefly to carve out a try through full-back Barry Davies, which was goaled by Gareth Bowen, but Glasgow snatched full control to kill off the Welshmen before the interval.

Scrum-half Graeme Beveridge claimed the first try after powerful charges by Gareth Maclure and Scott Lawson, with Howarth slotting the conversion and adding a quick penalty.

Bowen clawed back three points, but the Scarlets had no answer as Glasgow stepped up the pace in lethal style.

Logan burst into the contest, latching on to a long Howarth pass to score under the crossbar.

Then Howarth jinked over for a brilliant solo effort which featured two sidesteps.

Even better was to come on the stroke of half-time when Logan burrowed through in the corner, with Howarth keeping up his 100% conversion record.

He kicked his fourth penalty just after the restart as the Scarlets continued to toil, but they refused to fly the white flag and sub Salesi Finau collected a long-range try with Bowen adding the extras.

Scrum-half Mike Phillips followed suit as Glasgow took their foot off the pedal – and the jitters set in when Murray was dismissed.

They were reduced further as Fergus Thomson was sin-binned – and Garan Evans slid over to salvage a late consolation point for Llanelli.