The two-time Wimbledon finalist fired 17 aces and did not face a break point Tuesday in his first-round match against 60th-ranked Schwank on Court 1.
Roddick converted only two of 12 break-point chances in a tough, grinding match before dominating the tiebreaker to close it out.
Roddick will meet Janko Tipsarevic in the next round.
Rafael Nadal — coming off his fourth straight French Open championship and first grass-court title — got off to a solid start on Centre Court in the first round of Wimbledon on Tuesday.
Runner-up to Roger Federer the past two years, the second-seeded Spaniard beat 122nd-ranked German qualifier Andreas Beck 6-4, 6-4, 7-6 (0).
Nadal, who never faced a break point, managed to break Beck just twice out of nine chances. He saved his best for the tiebreaker, ripping a crosscourt forehand winner for 5-0, serving his 17th ace for 6-0 and forcing an error on match point with a backhand drop shot.
“The first match is always very difficult, but I played well in the last tiebreak,” Nadal said. “I was a little bit nervous today. It was tough, but I have very nice memories from the last two years.”
In the day’s first major upset, fourth-seeded Davydenko was knocked out in the first round in straight sets by 116th-ranked German Benjamin Becker, 6-4, 6-4, 6-4. It was the fifth time in seven years the Russian failed to get past the first round; he reached the fourth round last year.
“He played good, but I played very bad,” Davydenko said.
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