Vukic had been on a bad trot, having lost his first-round matches in his last four tournaments on the clay-court swing, but he overpowered the doughty Argentine 6-2 6-2 on Wednesday to become the first of the six-man Australian contingent to progress in the main draw.
The 31-year-old battler Schwartzman, a former world No.8 who's sunk to 142 in the rankings, had announced at the weekend that he plans to retire early next year back in Argentina but planned to enjoy one final season at the venues he enjoys most.
Unfortunately for him, Vukic was not about to indulge in any sentimentality as he ruthlessly put an end to Schwartzman's run through qualifying into the main draw of the Masters 1000 event.
The 28-year-old Australian gleaned five break points throughout the match and converted four of them, while Schwartzman couldn't take advantage of any of his own eight break points as Vukic held firm.
Vukic got the job done to set up a much more daunting second-round encounter with Olympic champion Alexander Zverev, who beat the Aussie in straight sets at last year's US Open.
Biggest surprise of the day was Argentine-born Italian Luciano Darderi beating  Canadian leftie Denis Shapovalov on Campo Centrale 6-7 (4-7) 6-3 7-6 (7-4), while Brazilian qualifier Thiago Monteiro knocked out French veteran Gael Monfils 6-2 7-5.
Rafael Nadal, the record 10-time Rome champion, opens against Belgian qualifier Zizou Bergs on Thursday, while top-ranked Novak Djokovic, back in Rome after a month out, is in the opposite half of the draw.
World No.2 Jannik Sinner and No.3 Carlos Alcaraz both withdrew from the event, the last major warm-up before the French Open, because of injuries.
Australia's challenge will continue on Thursday when Sydney's Alexei Popyrin meets Serbian qualifier Hamad Medjedovic in the first round.
