It took only until the fourth game for the Vukic serve to be breached, as Sinner converted his fourth break opportunity, having saved one on his own delivery in the previous game.
The double-break was secured at 5-1, before a love-hold closed out the opener in just 28 minutes.
The second set started in the same vein as the first, with Sinner breaking Vukic immediately, before racing into a 5-1 lead, forcing the world No93 to serve to stay in the set.
He couldn’t - broken for a third time in the second - and Sinner was riding off into the sunset.
The third - and what proved to be the final - set was a tad more competitive, with Vukic making the scoreline slightly more respectable.
Both players traded holds until the eighth game, where Sinner decided to turn the heat up a tad more.
He ruthlessly took his only break point, but he made a meal of serving it out, needing six match points to get the job done, but not before staving off a break-back point.
Sinner marches on relentlessly, however, and he will face Martinez, who conquered Briton George Loffhagen in his opener, in the third round.
Martinez, the world No52, beat Mariano Navone in straight sets on Court No15 to earn his meeting with the reigning Australian Open and US Open champion.
