At the start of a critical period for Glasgow's hopes of finishing in the league's top four and qualifying for the play-offs, the Warriors were tested by their Welsh opponents despite their domination of possession and territory.
Glasgow, who led 11-3 at the break, scored the only try of the night in the 31st minute, when live-wire winger Nikola Matawalu crossed with Duncan Weir adding three penalties.
Scarlets had little possession to engineer much in the way of attacks, but defended securely with their points coming from a brace of Olly Barkley penalties.
The Warriors dominated possession from the start and when referee Alain Rolland detected a high tackle on centre Alex Dunbar in the eighth minute, stand-off Weir opened the scoring with a penalty. Glasgow made nothing of further possession particularly when they chose to put a penalty into touch on the visitors' line but midway through the half Scarlets were penalised for off-side and Weir kicked the simple penalty to make it 6-0.
Six minutes later, hooker Doug Hall's throw was not straight and Scarlets produced a position close to the Glasgow line. The Warriors were then penalised at the subsequent scrum and Barkley opened the visitors' account. The home side returned to the attack, helped by Rolland continuing to penalise Scarlets at the tackle, and Matawalu touched down.
Again, Glasgow had turned down a chance to kick for the posts and the subsequent line- out drive sent Rolland to the television match official. The verdict was no try, but from the subsequent scrum, Matawlu, who despite being listed as a winger was popping up all along the back line, took the pass from scrum-half Chris Cusiter and cut through to score from 10 metres.
Weir's conversion attempt slipped wide, so Glasgow went in at half-time deservedly leading 11-3. Within the first 10 minutes of the restart, Weir and Barkley had exchanged penalties. Soon after Scarlets had replaced their complete front row, their scrum was penalised, but Glasgow's substitute centre Mark Bennett failed with the long-range penalty attempt.
As the final quarter began, the Warriors produced a prolonged period of scintillating passing and off-loading. However, Scarlets stoutly rebuffed the siege of their line which ended with Glasgow penalised at a close-in scrum.
Glasgow continued to press in the closing stages and Scarlets were in debt to right winger Kristian Phillips who got back to deal with a dangerous kick to his line. With three minutes left on the clock, Scarlets had the chance to claim a bonus point, but Aled Thomas's penalty went wide.
Glasgow: Murchie, Seymour, Vernon, Dunbar, Matawalu, Weir, Cusiter, Reid, Hall, Welsh, Swinson, Gray, Harley, Fusaro, Strauss. Replacements: Bennett for Dunbar (54), Jackson for Weir (52),
Yanuyanutawa for Reid (63), Brown for Hall (59),
Low for Welsh (59), Kellock for Swinson (59).
Scarlets: L Williams, K Phillips, J Davies, Barkley,
J Williams, A Thomas, G. Davies, John, Owens, Lee, Earle, Snyman, Turnbull, Barclay, Timani. Replacements: A Warren for L Williams (77),
Maule for Barkley (63), R. Williams for G Davies (59),
R Evans for John (50), E. Phillips for Owens (50),
R Jones for Lee (54), Kelly for Earle (69),
Ball for Snyman (54).
Referee: Alain Rolland (Ireland).