Millman won the match in two straight sets.
Ymer, however, offered a real fight in the second, the set numbers were written to 6-2, 7-6.
Ymer made it to the second round by first defeating two Americans in the qualifiers and then also 62-ranked Australian Jordan Thompson with 3-6, 7-5, 6-3 in the first round.
In the third round, the winner between the American Reilly Opelka and Daniel Elahi Galan Riveros from Colombia is waiting for Millman.