Schwartzman, seeded 24 in Melbourne, showed no signs of fatigue after his five-set marathon victory over Dusan Lajovic on Monday, beating qualifier Ruud 6-4, 6-2, 6-3.
Although sending down fewer aces (6-9) and serving more doubles faults (4-2) than his Norweigian opponent, Schwartzman of Argentina came into his own in the all-important first-serve points won static, with an impressive 89 per cent. He also converted six out of 11 break points, with a fastest serve measuring 164kph.
Schwartzman awaits the winner of the match between Matthew Ebden and Alexandr Dolgopolov in round three.
Another Jewish player, Camila Giorgi, will be looking to reach round three in the Ladies Singles tomorrow when she takes on local favourite Ashleigh Barty.