The world No 1 was playing a singles match for the first time since his shock loss to Mischa Zverev in the fourth round of the Australian Open five weeks ago.
He revealed ahead of the tournament that he was laid low by a bout of shingles following his return from Australia but looked in decent form here.
Murray made a slow start and struggled to find his first serve but he got better as the match went on and emerged a comfortable 6-4, 6-1 winner.
The 29-year-old looked jaded in Melbourne having had little time to recover and reset after his phenomenal end to 2016.
An early-season rest was very welcome, therefore, and good timing with no threat to his No 1 ranking on the horizon.
The first set was anything but comfortable for Murray, with 51st-ranked Jaziri playing with freedom and taking advantage of his opponent’s difficulties on serve.
The Tunisian, in the best form of his career at 33, broke for 2-1 on a very fortuitous net cord but Murray hit straight back and broke serve again to win the opening set.
Although the Scot’s first-serve percentage languished at 40, he was in total control in the second set and wrapped up victory inside an hour and 20 minutes.
Jaziri bizarrely called for the trainer at 0-40 in the fourth game, resuming after a brief conversation, but did not win another game.
Afterwards, Murray said: “I have never hit with him or played against him before.
“It took a little bit of time to get used to his game. But I played better as the match went on.”
The Scot landed only 40 per cent of his first serves but overcame the low percentage by defending his second serve well, taking nearly 70 per cent of those points (19/29). Murray was broken once but converted four of his eight break-point opportunities against Jaziri, who reached the Dubai quarter-finals in 2014.
Murray added on atpworldtour.com: “The only thing I didn’t do well was the first serve… I’m not sure exactly why.
“Maybe first match under the lights, haven’t practised in those conditions since I have been here.
Murray will take on Spaniard Guillermo Garcia-Lopez in the last 16 today.
Fellow Brit Dan Evans continued his fine form in 2017 with a first-round victory over Dustin Brown in Dubai.
The British No 2 took a break after helping Great Britain to victory over Canada in the Davis Cup three weeks ago, which came on the back of a first ATP Tour final in Sydney and a run to the fourth round of the Australian Open. But Evans, who is at a career-high ranking of 43, showed no signs of rust as he brushed aside unorthodox Jamaican-German Brown 6-2, 6-3 in 51 minutes.
The 26-year-old was dominant on serve, dropping just five points, as he set up a second-round clash with fourth seed Gael Monfils.
In the opening round of the Malaysian Open, Elina Svitolina continued her winning run.
The Ukrainian lifted the biggest title of her career on Saturday by beating Caroline Wozniacki in the final of the Dubai Duty Free Championships to break into the top 10.
She had little trouble making it 13 victories in a row in Kuala Lumpur, beating qualifier Jang Su-jeong 6-2 6-3.