And the classy Jones managed to put his stamp on the game by converting Deacon Manu's try and adding the extras to his own 74th minute touchdown as the Scarlets left Connacht stunned.
Connacht's Ian Keatley had been winning his fly-half battle with Rhys Priestland, kicking two penalties and a drop goal and also racing through for a 46th minute try.
However, the Ireland 'A' international also missed two kickable penalties and a conversion as Connacht's 14-3 lead was overhauled in the final quarter by the Jones-inspired visitors.
After the wind-backed Scarlets established an early foothold in the hosts' half, Priestland converted a fifth-minute penalty for the lead score.
But Nigel Davies' men were lacking ideas and as the half progressed, Connacht swung possession in their favour.
After a flat opening, Connacht sprung into life thanks to a 30-metre break from number eight Colm Rigney. That cameo and a brilliant turnover from captain John Muldoon helped set up Keatley's successful first penalty of the night.
The province's place-kicking hero against Munster, he added his second penalty on the half-hour mark before missing a much easier penalty attempt.
Before Keatley's miss, Niva Ta'auso barged through the visitors' midfield and into the 22 and the Samoan centre was then involved in setting up a late dart at the line for Fionn Carr.
The Scarlets also had a short spell of dominance before the break, gobbling up the yards before winger Darren Daniel was stopped five metres out.
Connacht wasted little time in improving their 6-3 half-time lead. The second half was just six minutes' old when full-back Gavin Duffy sliced his way up to the Scarlets' 22, Mike McCarthy carried forward and then Keatley dummied and burst clear for a smartly-taken try.
Connacht coach Michael Bradley called for his players to learn 'how to close out games' after losing at Leinster last week. When Keatley tagged on a drop goal for 14-3, they looked well set for the win.
Unfortunately for the vocal home support, Connacht let their composure slip and with Priestland at full-back and Jones directing operations behind the pack, the Scarlets marched forward.
Frank Murphy and McCarthy both made costly errors and after Jones kicked a penalty to touch, prop Manu muscled over the whitewash after a lineout catch and drive.
Emptying their bench, the Scarlets introduced French recruit Yannick N'Gog and the fresh legs helped work Jones over for a crucial try. He nailed the conversion and Connacht's frustrations deepened when Keatley missed a subsequent penalty and a Duffy drop goal attempt sailed wide.