In an error-strewn match the Scarlets struggled to put away last year's basement boys, but Newton's boot plus second-half tries from prop Rhys Thomas and wing Andy Fenby ensured a satisfactory start to the campaign for the West Walians.
Both sides went into the match decimated by World Cup calls. The Scarlets were minus 10, including their entire first-choice back division, while the Italians have 11 out in New Zealand.
And it was Aironi, who propped up the table in their first season of Celtic rugby, who took an eighth-minute lead through a penalty from new South African acquisition Naas Olivier.
With the Scarlets scrum in the ascendancy, Aironi did well to withstand pressure on their own line, holding up number eight Ben Morgan just short.
But after a half break by the fit-again Fenby, fly-half Newton levelled matters on 23 minutes.
With heavy rain ruining the game as any sort of spectacle, the Scarlets were struggling to get their running game going and were punished again on 26 minutes by the boot of Olivier.
Newton made it 6-6 after a break by centre Rhodri Gomer-Davies, then put his side in front for the first time seven minutes before half-time as Aironi continued to infringe.
It led to scrum-half Tito Tebaldi being shown a yellow card, although the Italians were able to hold out until half-time just 9-6 down.
Aironi were back on level terms six minutes after the restart with a third penalty from Olivier.
Parc y Scarlets, though, finally came to life shortly afterwards with a superbly-crafted try by the home side from deep inside their own half.
Hooker Emyr Phillips made the initial burst down the touchline before the impressive Morgan powered through some fragile Aironi defence.
When the ball came wide, a couple of miss passes released prop Rhys Thomas hanging out on the wing and he finished off with a Chris Ashton-esque swallow dive in the corner.
Newton converted brilliantly from the touchline and suddenly the Scarlets had breathing space.
With the rain relenting, the home side started to take a stranglehold on proceedings and Newton extended his side's lead on 63 minutes with another penalty success.
A bullocking run from Rhys Thomas to the shadow of the posts gave Newton the opportunity to make it 22-9 to the Scarlets
And with three minutes remaining Fenby sent the Scarlets faithful home contented when he stripped the ball from the tiring visitors' to dive over.
Newton added the extras and his replacement Rhys Jones put a gloss on the scoreboard with three more points with the last kick of the match.
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