The Scarlets secured their place in next year's Heineken Cup after a bonus-point Magners League win in Glasgow.
A dominant 15 minutes after the break proved decisive, Ben Morgan, Lou Reed and Tavis Knoyle crossing for tries.
Morgan Stoddart scored two first-half tries, but DTH van der Merwe's try and two Ruaridh Jackson penalties kept the home side in touch at 11-12 down.
Van der Merwe added another early in the second half before Tom Ryder's late consolation ended the scoring.
With a place in Europe's premier cup competition available to the three highest placed of the four Welsh regions in the Magners League, the Scarlets are now guaranteed to finish above Newport Gwent Dragons, who lost to Edinburgh on Friday night.
There were promising signs for an open, entertaining end-of-season encounter as both sides crossed the tryline inside the opening 20 minutes.
The Scarlets drew first-blood when Stoddart crossed in the left corner after Scott Williams had charged through the home defence.
Williams, the highly-rated 20-year-old centre, started the move by forcing a turnover, and he then showed more strength by bouncing off two would-be tacklers before offloading to Stoddart on his outside shoulder.
Stephen Jones' conversion put the visitors 7-6 ahead - Jackson having opened an early lead for Glasgow with two penalties in the first 10 minutes - but the home side responded with a try within two minutes.
Winger Van der Merwe started and finished the move, making amends for his weak tackle on Williams which led to the Scarlets try.
Jackson missed the conversion from the right touchline, and the fly-half then missed two relatively simple penalty attempts.
Those poor kicks came when the Scarlets were down to 14 men after lock Reed was sent to the sin bin for a petulant throw of the ball to the face of Glasgow scrum-half Chris Cusiter.
That episode typified the drop in the standard of play after the initial creativity, but the Scarlets managed to re-group just before the break to score a second try.
Winger George North wasted a glorious opportunity to cross when he dropped the ball with the line at his mercy, but Stoddart again showed his finishing prowess by forcing himself over in the corner after a clean midfield break from number eight Ben Morgan.
Jones missed the conversion, meaning the visitors led by just a point at the break.
That slender advantage, though, lasted less than two minutes of the second half as Van der Merwe touched down in the left corner.
North was the guilty party as he lost possession inside his own half, giving Glasgow a perfect counter-attacking platform, and Van der Merwe slipped out of Aaron Shingler's desperate dive before withstanding Stoddart last-ditch charge.
Jackson rediscovered his kicking boots to add the extra two points from the left touchline, but the Scarlets were soon on level terms as Jones stroked over two penalties from in front of the posts.
The second opportunity came following Moray Low's off-the-ball tackle on Johnathan Edwards, a senseless infringement which landed the prop 10 minutes in the sin bin.
Jackson's third penalty briefly put Glasgow back in front, but the visitors exploited their numerical advantage when a perfect rolling maul from a lineout five metres from the home tryline gave Morgan the simplest of task to dive over. Jones missed the conversion.
Glasgow again got their noses in front with Jackson's fourth penalty, but the Scarlets responded in style to score their fourth try and secure a bonus point.
North made amends with a superb catch from Jones's re-start, and after a couple burst from the forwards towards the home tryline, there was no-one left to stop Reed, another first-half sinner, from crashing over.
The conversion was a formality for Jones, putting his side 24-30 up with less than 20 minutes to go.
Knoyle completed a dominant 15 minutes when he scored under the posts for a superb team try which saw the Scarlets keep possession inside the Glasgow 22 for 19 phases. Jones converted, to open a 13 point lead.
Ryder's try with six minutes remaining gave Glasgow slender hope of an unlikely comeback, but the Scarlets held on with ease to secure a hugely satisfactory trip north.
Glasgow: Bernardo Stortoni, Hefin O'Hare, Peter Murchie, Graeme Morrison (capt), DTH van der Merwe, Ruaridh Jackson, Chris Cusiter, Kevin Tkachuk, Dougie Hall, Moray Low, Aly Muldowney, Tom Ryder, James Eddie, Richie Vernon, Johnnie Beattie.
Replacements: Fergus Thomson, Jon Welsh, Ryan Grant, Robert Harley, Ryan Wilson, Duncan Weir, Colin Gregor, Federico Aramburu.
Scarlets: Morgan Stoddart; George North, Gareth Maule, Scott Williams, Sean Lamont; Stephen Jones, Tavis Knoyle; Iestyn Thomas, Matthew Rees (capt), Rhys Thomas, Lou Reed, Aaron Shingler, Rob McCusker, Johnathan Edwards, Ben Morgan.
Replacements: Emyr Phillips, Phil John, Simon Gardiner, Dominic Day, David Lyons, Martin Roberts, Rhys Priestland, Daniel Evans.
Referee: Carlo Damasco (Italy)
Assistant referees: Andy Ireland, Achie McInally (Scotland)
TMO: Jim Yuile (Scotland)