Even though Munster were missing 12 players on Irish World Cup training duty as well Rob Henderson and Jason Holland, Bowen was the star of the show and ensured the Welsh continued their winning start in this year's Celtic League.
The visitors dominated much of the first half but failed to turn possession into points. Despite seeing Jeremy Staunton successfully kick a penalty in the seventh minute, the Scarlets spent the next 23 minutes camped deep inside the Munster 22.
But their continued pressure only garnered one penalty from Bowen and when the Munster finally broke out of their own half, Staunton put Munster back in front with another penalty that gave them a 6-3 half-time lead, although not before Llanelli flanker Ian Boobyer was sent to the sin bin for a deliberate offside.
The visitors started the second half in much brighter fashion, Bowen sending over a 43rd minute drop goal to bring the sides level. Prop John Davies became the second Scarlet to see yellow, and he was soon followed into the sin bin by Munster flanker Denis Leamy. Before Bowen and Staunton exchanged penalties to leave the scores level at 9-9 with an hour gone.
The game leaned in Llanelli's favor when Killian Keane's defensive clearance was charged down by opposite number Bowen, who collected the ball to score close to the posts, converting his own try to open up a 16-9 lead. Staunton was able to close the gap to 16-12 with a penalty from under the posts but that was how it stayed.
With Munster once again defending inside their own half, Quinnell failed to rise from the bottom of a ruck and after lengthy medical attention on the field before being stretchered off. It meant there was plenty of injury time and Munster used it to push hard up field.
But Llanelli managed to turn the ball over, kicked back up field and won a penalty which Bowen kicked successfully to bring Munster's proud record to an end.
Commenting on the win Scarlets captain Leigh Davies was keen to praise his young team after the historic win.
"If you could see the delight on the boys faces in the dressing room - a lot of them are young and haven't seen anything like that,"
"They had 12 internationals out, but we were missing 10. "We've got a great squad here and the World Cup boys will have to fight for their places when they get back, Gareth Bowen was outstanding.
Final Score: Llanelli 19 Munster 12
Munster Pens: J Staunton (4).
Llanelli: Try: G Bowen. Con: Bowen. Pens: Bowen (3). DG: Bowen
Munster: Jeremy Staunton; Mossie Lawlor, Mike Mullins, Jason Jones-Hughes, Shaun Payne; Killian Keane, Eoin Reddan; Simon Kerr, Jerry Flannery, Martin Cahill, Trevor Hogan, Eddie Halvey, Denis Leamy, David Wallace, Jim Williams (capt).
Replacements: Martin McPhail, Colm McMahon, Frank Murphy, Stephen Keogh, Donal Sheahan, Andy Long, Jody Danaher.
Llanelli Scarlets: Barry Davies; Tal Selley, Matthew J Watkins, Leigh Davies (capt), Dale Burn; Gareth Bowen, Mike Phillips; David Maddocks, Aled Gravelle, John Davies, Adam Jones, Chris Wyatt, Emyr Lewis, Ian Boobyer, Scott Quinnell.
Replacements: Nathan Williams, Rhys Williams, Bryn Griffiths, Vernon Cooper, Lee Byrne, Ceiron Thomas, Gavin Evans.