Schwartzman of Argentina, the competition's 24th seed, followed his first round win over Peter Ebden with a solid performance against Koepfer, beating the German in straight sets.
The first set was a one-sided affair, with Schwartzman running away with it to win 6-0.
Koepfer gradually came into the match, but ultimately Schwartzman's consistency told as he won the next two sets 6-3, 7-5 in a contest where Koepfer outgunned his opponent on aces (7-3), as well as double faults (7-1). He also hit twice as many unforced errors as Schwartzman (54-27).
Things will get harder for Schwartzman in round three where he faces 17th seed Matteo Berrettini of Italy. The winner could face eight-time champion Roger Federer in round four.
