The Scarlets produced glimpses of the sort of form needed to compete in Europe. Simon Easterby continued to impress, but he is too often a one-man band.
The home fly-half Bowen and his opposite number Dan Parks traded penalty goals for the first 30 minutes to leave the Scarlets ahead 9-6 before the Glasgow scrum-half Sam Pinder was shown a yellow card. The Scarlets lock Hottie Louw immediately lumbered over the line for the game's first try on the stroke of half-time.
Parks narrowed the margin with his third goal, before the Scarlets' Liam Davies took the ball at the base of a ruck five metres out and darted over.
Glasgow's Gregor Hayter then ran 20 metres untouched for a try and Parks' fourth goal narrowed the margin to four points.
The two kickers traded penalties and some desperate defence in injury time helped the Scarlets to limp over the line.
Llanelli Scarlets: Tries Louw, L Davies; Conversion Bowen; Penalties Bowen 4. Glasgow: Try Hayter; Penalties Parks 5.
Llanelli Scarlets: L Byrne (G Evans, 67); D James, M Watkins, R King, M Jones; G Bowen, L Davies (C Stuart-Smith, 67); I Thomas, A Gravelle (M Rees, 40), R Davies, I Afeaki (C Wyatt, 50), H Louw (A Jones, 50), J Mills, A Popham, S Easterby (capt). Glasgow: R Lamont (C Gregor, 80); M Roberts, A Craig (G Morrison, 57), A Henderson, H O'Hare; D Parks (capt), S Pinder (G Hayter, 46); L Harrison, S Lawson (F Thomson, 72), E Murray (K Tkachuk, 40), C Hamilton, T Barker, P Dearlove (S Swindall, 64), A Wilson (G Beveridge, 40), J Beattie.
Referee: D Courtney (Ireland).
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