Roddick didn't have it all his own way on Court 1 against the left-handed Beck, but his serve kept him in control. The three-time runner-up at Wimbledon had 30 aces — including four in a row to win a game in the first set.
Beck had a chance in the second-set tiebreaker when he led 5-4 with two serves to come, but overhit a backhand and Roddick took advantage.
The eighth-seeded American went on to seal his 11th straight first-round win at Wimbledon. The match was held over from Monday because of rain.