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.
Jonathan Erlich of Israel bowed out in the first round of the Men's Doubles, when he and partner Artem Sitak lost against ninth seeds Maximo Gonzalez and Horacio Zeballos. The Argentinian duo won 7-5, 7-6, 6-3.
