Former All Black centre Regan King - one of the best players in the League this season - scored two tries in the opening 10 minutes, but the Scarlets were trailing 26-25 before Mike Hercus snapped up an intercept and Jones out-sprinted the visiting defence.
Reivers inside centre Calum MacRae sneaked a penalty goal in off an upright to open the scoring in only the second minute, but it proved to be a false dawn as the Scarlets moved up a gear. Several attacks on the Reivers' line splintered the Scottish defence and King continued his superb season with a try in the corner. Fly-half Mike Hercus missed the extras but added a penalty goal, and a stunning Peel break and some good work from new Ospreys signing Lee Byrne put King over for a try double in the space of five minutes.
Just as the Scarlets looked like producing a cricket score, the constant showers affected handling and Jenkins's men went off the boil. Skipper Dafydd James was dragged down an inch short of adding a third try, but that was as close as the home side got to adding to their total, and two MacRae goals narrowed the margin to 15-9 at the break.
Whatever Scarlets and Wales coach Jenkins said at halftime was still ringing in the Scarlets players' ears when their Kiwi prop Craig Dunlea powered over the try-line. Reivers No.8 Kelly Brown silenced the fans by galloping down the touchline for an immediate reply, and it was "game on" when the visitors' replacement backrower Semo Sititi scored.
Reivers fullback Stuart Moffat swept the visitors into the lead with a stunning break and pass for Charlie Hore to score, but Hercus intercepted a promising Reivers move and Jones raced 80 metres for the winning score and a bonus point.
Tries - R King 2, C Dunlea, M Jones
Pens - M Hercus 2
Cons - M Hercus 2
Tries - K Brown, S Sititi, C Hore
Pens - C MacRae 3
Con - C MacRae
Halftime: Llanelli Scarlets 15-9
Referee: Peter Fitzgibbon (Ireland)