Defending champion Jack Sock reached the Delray Beach Open second round, while Hyeon Chung also advanced on Monday.
Sock broke once in each set on his way to a 6-4 6-4 victory over Australian qualifier John-Patrick Smith.
The American top seed only created two break points - converting both - while saving four to get through his opener.
In action for the first time since his run to the Australian Open semi-finals, Chung - the eighth seed - got past lucky loser Cameron Norrie 3-6 6-3 6-1.
Meanwhile, Donald Young crushed Ramkumar Ramanathan 6-1 6-2 and Frances Tiafoe overcame Matthew Ebden 6-2 2-6 6-2.