After last weekend's nail-biting 20-19 win over Toulouse at Stradey, the Scarlets showed tremendous mental strength to claw their way back after Toulouse fullback Clement Poitrenaud bagged a hat-trick inside 30 minutes in his four-try haul.
Jones landed his first penalty just 90 seconds from kick-off, but it was all Toulouse for the opening half an hour.
Inside-centre Florian Fritz brushed off Regan King's attempted tackle to put Poitrenaud over for his first try, converted by Valentin Courrent, after just three minutes before dropping a goal from 30 metres out.
Then a flowing move down Llanelli's right flank saw Poitrenaud pop up for his second try, again converted by Courrent, and the home side were cruising at 17-3 with less than 20 minutes played.
The hat-trick was completed after a Scarlets turnover and centre Maleli Kunavore, in for flu victim Yannick Jauzion, chipped down the flank and Poitrenaud gathered and sprinted over to put his side 24-3 up.
Crucially the guests gave themselves a precious lifeline as King slipped a pass to send Dafydd James over; Jones's conversion brought Llanelli back to 24-10 at the break.
Yet it was business as usual after the interval as Poitrenaud side-stepped opposite number Barry Davies to put his side 31-10 up just seven minutes into the second-half. Now was the time for theScarlets' fightback.
Scarlets No.8 Popham gave his side a glimmer of hope after gathering his own kick ahead to feed Darren Daniel for a valuable try with Jones landing the tricky conversion.
A quick break by Dwayne Peel saw fullback Davies hand off the defence to go over as the Scarlets bagged two tries in four minutes to put them just a converted try behind.
Jones and Courrent swapped penalties to make it 34-27 with 20 minutes to go.
The travelling fans were lending their vocal support and the Scarlets were back on level terms at 34-all when King's delicate chip through was missed by Cedric Heymans and Daniel pounced on the loose ball for his second try on 66 minutes.
It gave the guests the bonus point, but the Scarlets were finding big holes in the Toulouse defence and anticipation of an upset spread through the crowd.
Jones landed the difficult conversion from out wide, but Toulouse piled on the pressure as ex-Ireland flanker Trevor Brennan was held up before Fritz went wide with a drop goal.
Yet the Scarlets wrote themselves into the history books and became the first side to beat Toulouse at home in Europe since 2000 when ex-All Black King carved his way through the defence and popped the ball to Nathan Thomas for Llanelli's fifth try.
When referee Chris White blew for full-time, it capped arguably the best fightback in Heineken Cup history.