The 34-year-old Agassi dominated the opening set against Czech Michal Tabara but had to work in the second set to claim a 6-2, 7-6 victory.
"The second set could have gone either way," said two-time champion Agassi, who is making his first clay-court appearance of the season.
Agassi admitted that facing an opponent he had never played worked against him at time.
"Never playing each other makes it slightly uncomfortable," he said. "It's nice when you have a better sense of what a guy does well.
"I was pretty frustrated through the middle of the second set on," Agassi said. "I had some love 30 chances and I never stepped up. I felt like I waited and he took it to me."
The two-time champion will face Spaniard Alex Calatrava in the second round of the tournament, which Agassi said is bringing back fond memories.
"This is where I became the oldest No. 1 player two years ago, so it stands out as a very memorable time," he said. "It was a big accomplishment for me."
Roddick turned back American qualifier Matias Boeker in straight sets, 6-2, 6-3.
"I had one sloppy game where I missed a couple of balls I felt I should have made, but overall it was a solid performance," said Roddick, the runner-up in Houston the past two years.
"I got to the ball with enough time to do something with it, which is especially key on this surface," said Roddick, who will play fellow American Robby Ginepri on Wednesday.
Defending champion and third-seeded Tommy Hass of Germany also won. He defeated Belgian Kristof Vliegen 6-3, 7-5.
