The Scarlets' brave bid for a place in the Magners League play-offs ended in a bittersweet disappointment despite this bonus-point win over Cardiff Blues.
The Ospreys' 12-10 win in Aironi ensured them a play-off spot, but the Scarlets could have done no more against a side that also went into the game harbouring play-off hopes.
Iestyn Thomas, Ben Morgan and Sean Lamont (2) went over for the hosts.
Chris Czekaj and Dafydd Hewitt touched down for the visitors.
Having lost against Newport Gwent Dragons the previous week, the Blues had to beat the Scarlets in order to secure a play-off spot.
The Scarlets struck first, fly-half Jones profiting from their early monopoly of possession to set up the penalty chance.
Parks hit back against the run of play only for Jones to put his side back into the lead after setting up the chance with an up-and-under that fell into Czekaj's arms as the Wales veteran arrived to bring him down.
Better was to come for the hosts. After prop Iestyn Thomas' touchline charge ended with his foot going into touch the veteran went over in a more traditional manner.
Blues' Michael Paterson's late, high tackle on fly-half Jones gave the victim the chance to kick another penalty as the visiting lock was banished to the sin bin.
Instead Scarlets' skipper Matthew Rees opted for a close-range line-out drive against a depleted pack and that brought its reward as Thomas emerged from a pile of bodies to claim the try.
Jones converted from the touchline, belying the blow he had just taken. However, having dominated territory and possession while taking advantage of the Blues' poor defence the Scarlets were soon to suffer a reversal of fortunes.
Jamie Roberts - making a rare right-wing appearance - came off his flank to make the time and space to send Czekaj past George North, Parks converting.
The pendulum swung in the other direction after Parks added a penalty when McCusker was penalised for shoulder charging Czekaj as both attempted to gather a high ball.
Impressive Scarlets number eight Ben Morgan went over after they pounced on another Blues mistake, crashing past Richie Rees' attempted tackle to score under the posts, Jones converting.
At the other end Dafydd Hewitt went over after Morgan brought the centre down, but without holding the Blues centre, who sprang off the floor to score, Parks adding the extra points.
Three minutes from the break, fly-half Jones succumbed to the effects of the blow suffered on Paterson's shoulder and the teams were level 20-20 at the break after Parks missed a last-gasp drop-goal.
The Scottish international made amends two minutes after the break, then the Blues suffered their own big blow from a collision as Xavier Rush departed on a stretcher after mis-timing his tackle on prop Rhys Thomas.
Parks missed a 49th-minute penalty and Jones' replacement Rhys Priestland levelled with his first shot at goal four minutes later.
As Casey Laulala limped off the Blues' lost another catalyst and creator and their mettle was further tested when Sean Lamont went over after another sweeping Scarlets attack.
Flanker Martyn Williams earned a yellow card for his indiscretion at a tackle in the build-up to Lamont's score, adding to his side's woes.
Priestland edged the hosts further ahead with a penalty and Scotsman Lamont scored again to seal the bonus point as he stole away on the left.
Scarlets: Stoddart; North, King, S Williams, Lamont; S Jones, Knoyle; I Thomas, M Rees, R Thomas, Reed, Day, McCusker, J Edwards, Morgan. Replacements: L Williams for Stoddart (40), Priestland for S. Jones (37), Roberts for Knoyle (67), John for I. Thomas (74), Pugh for McCusker (37), Phillips for J Edwards (74).Not Used: P Edwards, Owens.
Cardiff Blues: Fish; Roberts, Laulala, Hewitt, Czekaj; Parks, Rees; Hobbs, G Williams, Filise, Paterson, Tito, Warburton, M Williams, Rush. Replacements: Robinson for Laulala (56), L Williams for Rees (61), Andrews for Hobbs (61), Molitika for Rush (45).Not Used: R. Williams, T Davies, D Jones, Sweeney.
Ref: Nigel Owens (WRU).