American Roddick is attempting to become the first four-time winner of the tournament. Andre Agassi is the only other player to win the event three times.
Fifth-seeded American Mardy Fish used 19 aces to beat Lleyton Hewitt of Australia 7-6 (5), 6-3 to advance to the second round. Former top-ranked Hewitt won the SAP Open in 2002.
Roddick, ranked No. 6 in the world, is looking for his title this year. He lost to Roger Federer in the semifinals of the Australian Open and lost to Andy Murray in the Qatar Open final.
Ryderstedt started serving better in the second set but Roddick dominated the 25-year-old in the tiebreaker.
"There wasn't a whole lot of rhythm to be had in the match,'' Roddick said. "He pretty much made up his mind that he was going to take a rip at most shots and he started to go for a bunch of big second serves in the second set.
"I did what I had to do to win. I almost worked my way out of a feel for how he was playing. It was almost backwards. It was tough. I got on him early but I wasn't doing a whole lot. And when he stepped up his game it was tough to get in the moment again.''
Nerves and the surface of the court played against Ryderstedt.
"I came through qualifying and the matches were held on a different surface and club,'' he said.
"Also, it's not everyday a 368th ranked player plays a No. 6 ranked player in such a big stadium every week. In the second set, I started to serve better and going for my shots more and it worked better.''
In other first-round matches, eighth-seeded Robby Ginepri was upset by fellow American, qualifier Todd Widom.
Widom won 3-6, 7-6 (2), 6-4 for his first victory in an ATP event since he won a first-round match at Delray Beach in January 2006. The 25-year-old Widom, ranked 270th, has battled through two bouts of eye cancer, two knee surgeries and an elbow injury since 2006.
"It feels really good,'' Widom said. "This was a step in the right direction. I played the big points and tried to take the match to him and succeeded. This last year, I thought my career was over because of the various injuries I had suffered.''
The 44th-ranked Ginepri hasn't won a match since Auckland Open in early January.
In other matches, Denis Gremelmayr of Germany needed three sets to beat Croatia's Roko Karanusic 3-6, 7-6 (4), 6-2; Australian Chris Guccione beat Guillermo Canas of Argentina 7-6 (7), 7-5 and Ernests Gulbis of Latvia defeated Brazilian Ricardo Mello 7-6 (4), 6-4.
Roddick wins first-round match
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