But from this point on Glasgow asserted themselves confidently to put the game out of reach for the Welsh side. Scrum-half Graeme Beveridge grabbed the first five pointer after some good work from Gareth Maclure and Scott Lawson, with Howarth slotting the conversion and adding a quick penalty.
Bowen clawed back three points, but the Scarlets' challenge wilted in the face of some stiff Scottish pressure. Logan stamped his mark on the game when he got on the end of a long Howarth pass to score under the crossbar. Then Howarth jinked over for a brilliant solo effort.
Logan soon grabbed his second, doing superbly to burrow his way over in the corner. Once again Howarth added the conversion. He soon added another penalty before the Scarlets showed some sign of life with a long range try from replacement Salesi Finau, 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.
Glasgow Rugby: Colin Shaw; Rory Kerr, Andy Craig, Gareth Maclure, Kenny Logan (capt)(2T); Calvin Howarth(1T, 4C, 4PG), Graeme Beveridge(1T); Kevin Tkachuk, Scott Lawson, Euan Murray (sent off 65); Andrew Hall, Dan Turner; Cameron Mather, Andrew Wilson, John Beattie
Bench: Fergus Thomson (sin bin 80), Andrew Kelly, Jonathan Van Der Schyff, John Barclay, Sam Pinder, Colin Gregor, David Millard. Replacements used: Kelly for Murray 49, Pinder for Beveridge 58, Gregor for Howarth 59, Murray for Kelly 59, Thomson for Hall 66
Llanelli Scarlets: Barry Davies(1T); Garan Evans(1T), Matthew Watkins, Tal Selley, 'Aisea Havili; Gareth Bowen(3C, 1PG), Mike Phillips(1T); Phil John, Matthew Rees, John Davies; Vernon Cooper (capt), Adam Jones; Jon Mills (sin bin 28-38), Gavin Thomas, Dave Hodges
Bench: David Maddocks, Aled Gravelle, Bryn Griffiths, Andy Powell, Chris McDonald, Aled Thomas, Salesi Finau(1T). Replacements used: Gravelle for Rees 41, Powell for Hodges 41, Finau for B.Davies 41, Maddocks for J.Davies 49, Griffiths for A.Jones 55, McDonald for Powell 76
Scoring sequence: 1' Howarth (PG) 3-0, 5' Howarth (PG) 6-0, 11' B.Davies (T) 6-5, Bowen (C) 6-7, 16' Beveridge (T) 11-7, Howarth (C) 13-7, 19' Howarth (PG) 16-7, 28' Bowen (PG) 16-10, 32' Logan (T) 21-10, Howarth (C) 23-10, 36' Howarth (T&C) 30-10, 39' Logan (T) 35-10, Howarth (C) 37-10, 44' Howarth (PG) 40-10, 49' Finau (T) 40-15, Bowen (C) 40-17, 57' Phillips (T) 40-22, Bowen (C) 40-24, 80' Evans (T) 40-29