Stevie Swindall scored two tries for Glasgow
Glasgow: (8) 30
Tries:O'Hare, Swindall 2, Tckachuk
Scarlets: (14) 14
Pen:C Thomas 3
Glasgow shook off their slumbers to continue their stirring Magners League revival by sweeping aside the depleted Scarlets at Hughenden.
The Warriors seemed a hesitant bunch in the first quarter, allowing the visitors to dictate the contest.
But they found their rhythm to seal another vital win, complete with a bonus point.
A brace from Stevie Swindall and single scores by Hefin O'Hare and Kevin Tckachuk put Glasgow on easy street.
Warriors looked the hungrier side during the jittery initial exchanges, but a combination of stout defence and careless handling prevented them from breaking through.
And, having survived the early storm, it was the visitors who edged in front with a crisply-struck penalty from 40 metres by outside half Ceiron Thomas.
Glasgow returned to attacking mode and yet more excellent tackling stopped their surge.
But some illegal handling on the deck gave Parks a simple opportunity to level the issue and he was never going to miss from almost underneath the crossbar.
The nervous sparring continued with both teams making mistakes galore and Thomas replied with his second accurate kick from closer range to restore the Scarlets' advantage.
Even better was to come for the visitors in the 17th minute when they snapped up an opportunist touchdown.
Matthew Watkins made the most of slack marking to pave the way for number eight Daffyd Jones to plough over from eight metres out.
Despite having the bulk of possession and territory, Glasgow found themselves further adrift when Thomas confidently completed his penalty treble.
Glasgow stepped up the pace in the approach to the interval and went within a fingertip of bagging a try.
Full-back Rory Lamont sprinted 40m before sending a chip across the goal-line. Hefin O'Hare was the chief chaser but he lost out to Daffyd James in the race to get the first touch.
The near miss served to inspire the Warriors and just two minutes later O'Hare was in the right place at the right time to squeeze over in the opposite corner following more slick stuff from Lamont.
Glasgow kept up the momentum after the restart and substitute scrum-half Sam Pinder almost wriggled across the line with his first touch of the ball, having taken a tapped penalty.
Scarlets captain James Bater was yellow-carded for a professional foul and seconds later another of the home bench-men, Stevie Swindall, powered over for their second score.
Parks made light of the wide angle to add the extra points.
Llanelli hit back in positive fashion with centre Regan King being hauled down just a couple of paces short of the target.
And they got their reward when Swindall completed his double, capitalising on excellent work by Pinder, Parks and John Barclay.
Parks was off the mark with the conversion bid, but made amends with a penalty to put the Scarlets out of the reckoning for a consolation point.
There was still time for prop Kevin Tkachuk to claim the bonus score, goaled by Parks.
Glasgow: Rory Lamont, O'Hare, Morrison, Henderson, Evans, Parks, Beveridge, Va'a, Tomson, Low, Newman, Kellock (capt), Petrie, Barclay, Beattie. Replacements: Gregor for Evans (29), Pinder for Beveridge (47),Tckachuk for Va'a (57), Turner for Newman (53), Swindall for Petrie (20), Barrow for Pinder (75)Not used:Milligan
Scarlets: B Davies; James, King, Watkins, Daniel; C Thomas, L Davies; I Thomas, Gravelle, Dunlea, A Jones, McLeod, Afeaki, D Jones, Bater (capt).
Replacements: Stoddart for B. Davies (60), G. Evans for Watkins (60), Stuart-Smith for L. Davies (75), Rees for Gravelle (51), Manu for Dunlea (37), G. Thomas for Afeaki (51)Not used:N. Thomas
Ref: Peter Fitzgibbon (Ireland)