The Scarlets scored six tries to five and despite a late comeback from the Falcons, an injury time score from Scott Quinnell sealed things in Llanelli's favour.
Gareth Bowen bagged 17 points with a try and 12 points to the boot while flanker Tal Selley scored a brace of tries.
Llanelli scorers: Tries - T Selley (2), B Griffiths, G Bowen, I Boobyer, S Quinnell
Cons - Bowen (5); Pen - Bowen
Newcastle scorers: Tries - M Stephenson, H Vyvyan, A Cadwalader, E Taione, P Dowson
Cons - B Gollings (2), J Shaw
Meanwhile, Cardiff Blues suffered a 29-6 home defeat to Northampton Saints, and to make matters worse, scrum-half Richard Smith was stretchered off with a neck injury.
The Blues were 7-3 down at half-time due to a try from Northampton, England and British Lions full back Nick Beal, Cardiff youngster Gareth McCarthy adding a penalty.
However, the floodgates opened in the second half as the Saints ran in four more tries from Chris Hyndman, Grant Seely, Jon Golding and Matt Lord with just one more McCarthy penalty to add to Cardiff's tally.
Cardiff Blues scorers: Pens - G McCarthy (2)
Northampton: Tries - N Beal, C Hyndman, G Seely, J Golding, M Lord
Cons - S Drahm, B Reihana