Roddick successfully landed 61 percent of his first serves to keep his Czech opponent off-balance throughout the one-hour match. He lost only one of 33 first-serve points.
"It's the only shot I was really hitting in the first set," Roddick said of his 12-ace performance. "I was hitting aces and when I was hitting good first serves they weren't coming back.
"I was really pleased with my serve tonight."
In a first-round match, 32-year-old Tim Henman lost to American wild card John Isner 4-6 6-4 7-6 after losing the third-set tiebreaker 7-4.
Roddick had little trouble with Zib although he had never played the 31-year-old Czech Davis Cup player ranked 151st in the world.
"Regardless of how the other person plays, you have to play to your strengths," said Roddick. "If you start playing someone else's game obviously it's not going to work as well.
BIG POINTS
"That being said you start studying what shots he likes to hit to what positions, which serves he goes for on big points. That's the stuff you learn as the match goes on."
The 24-year-old Roddick broke Zib once in the first set and twice in the second.
Despite a 38-10 record this year, including 24-6 on the hardcourts, Roddick said he was not yet ready for the upcoming U.S. Open.
"There's definitely stuff I have to work on," said the two-times champion of the Washington tour stop. "I feel like you always do before you hit your groove. You're on the verge of playing well."
Henman, who suffered a knee injury last October and had hamstring problems in January, saw his record fall to 5-10 this year.
"I don't feel there is anything wrong with my game," he said. "It's just disappointing to lose."
The 22-year-old Isner, a towering player at 6-foot-9, will play number eight seed Benjamin Becker in the second round.
"I have always wanted to play on centre court," said Isner, the world number 416. "I've never played on a stage like that."
