The American sixth seed, playing on a wild card as he seeks grass court practice after an early loss at Queen's last week, defeated Frenchman Jeremy Chardy 6-2 7-6 to continue a successful debut appearance on the south coast.
Chardy saved four match points in the 12th game of the second set and two more in the tiebreaker, before Roddick eventually came through with a winning backhand pass to win the breaker 8-6.
The former world number one, now ranked 33rd, ended a six-match losing streak with his opening win in Eastbourne this week, after a claycourt season which featured three losses in the team cup in Dusseldorf and one at the French Open.
"It was good, I served well and returned pretty well. He served great on big points, but I stuck through there," said Roddick.
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"I'm comfortable on this surface. I started playing really well in practice when I got here.
"If you ask me the reason, I'd give you a blank stare, because I have no idea how this game works and why it works, why all of a sudden I came out and I played three really good sets so far."
But other seeds tumbled as number two Marcel Granollers of Spain went down 6-1 4-6 7-6 to Uzbekistan's Denis Istomin.
Australian fourth seed Bernard Tomic led 5-2 in the final set but could not see out the win as Italy's Fabio Fognini emerged a 4-6 6-3 7-5 winner in their second-round contest.
Italian third seed Andreas Seppi is through after beating Carlos Berlocq 7-6 6-3, while Belgian Steve Darcis defeated former Australian Open finalist Marcos Baghdatis 6-4 4-6 6-4.