James Blake and Sania Mirza were among the winners on a rain-hit Tuesday at the Pilot Pen event in New Haven.
Showers wiped out the daytime session in Connecticut and only four matches were completed by the end of the day.
Third seed Blake beat unseeded Frenchman Arnaud Clement 6-4 6-2, and in-form American John Isner saw off Germany's Benjamin Becker 6-3 6-4.
"You just have to accept that you're not going to hit the 125 or 130 serve,"
"I took advantage of his second serves. In these conditions, being chilly and all, I knew he was not going to come up with Karlovic second serves."
Mirza defeated Anabel Medina Garrigues 6-3 6-3, and Poland's Agnieszka Radwanska outlasted Ai Sugiyama of Japan 7-6 (7-5) 3-6 6-4.