Haase next faces Colombia's Alejandro Falla, who defeated Poland's Lukasz Kubot 6-2, 3-6, 6-3, and Karlovic meets Lu Yen-hsun, who prevailed 7-6 (2), 6-7 (11), 7-6 (5) over Croatian qualifier Mate Pavic.
Also, Steve Johnson beat French lucky loser Albano Olivetti 6-4, 6-2. Tommy Haas was due to play the American but withdrew on Monday with a right shoulder injury.
Johnson next plays Russia's Teymuraz Gabashvili, who defeated Ukrainian Illya Marchenko 6-7 (9), 6-4, 7-6 (4).
Frenchman Gael Monfils beat Germany's Benjamin Becker 6-1, 7-5 for a second-round meeting with the fourth-seeded Kei Nishikori.