Much had been made of the injury to the Scots' influential Australian captain Tuipulotu in the build-up to the championship, but they still thrived without him on Saturday.
The Scots opened up a 14-0 advantage in the first 10 minutes and led 19-6 at the break through scores from Rory Darge, Jones and Ben White.
But Italy, who fought back from 22-10 down to defeat the Scots 31-29 in Rome last March, once again produced a spirited fightback, with the boot of Tommaso Allan and a breakaway try from Juan Ignacio Brex levelling things up at 19-19 heading into the final quarter.
But the Scots held their nerve to win their opening fixture in the Six Nations for the fifth year in succession as two further tries from Jones - Tuipulotu's trusty midfield sidekick for both club and country - took the game away from the Azzurri just as they were starting to scent a first win at Murrayfield for 10 years.
Scotland host champions Ireland next Sunday, while Italy will be at home on Saturday to Wales, who slipped to a 13th consecutive defeat in France on Friday.
"I'm pretty happy. It's not every day you get on the end of three. Thanks to the boys for setting me up," said Jones.
Scotland struck first when Darge barged over from close-range and then after a blistering break down the left wing from Duhan van der Merwe, the latter's pass inside was touched by Brex but fell perfectly for Jones to score.
Allan got the visitors on the scoreboard with two quick penalties as Italy settled into the game, but Scotland soon scored their third try.
Hooker Dave Cherry found his jumper in the lineout and wrapped around to carry the ball forward in a driving maul before setting White away with a superb offload as Scotland led 19-9 at halftime.
Allan kicked another penalty to narrow the gap to seven points early in the second period, and the visitors then drew level with their first try.
Finn Russell's poor pass was intercepted by Brex and the centre raced clear to score under the posts.
The momentum was with Italy and Scotland needed to wrestle it back, which they did on the hour-mark as wing Darcy Graham burst through a gap in the Italy defence and fed Jones to cross for his second score.
When Jones showed his power to hold off two defenders and stretched to complete his hat-trick Scotland had breathing space on the scoreboard.
With Reuters
