However, Roddick suffered an abdominal muscle strain late in the match and is considering withdrawing from the event with the U.S. Open looming large next month.
"I hit the one passing shot and strained something in my side," a subdued Roddick told reporters. "It doesn't feel too good right now.
"If it's like this tomorrow, I don't think there's a lot of hope.
"Once it happened, it was always there. When I served, and pretty much on every shot, there was pretty intense pain.
"I didn't play my best stuff but I got through tonight," added the world number 10, who unleashed 21 aces before setting up a last-eight meeting with Russian Dmitry Tursunov.
Wild card Oudesma, playing only his second ATP event, matched Roddick with power serves and crunching ground strokes in the opening set but lost momentum as his more experienced opponent upped his game.
"He served pretty big and I was unhappy with the way I played tonight," added Roddick, who has not won a title this year and dropped out of the top 10 in the rankings this month for the first time since 2002.
Fourth seed Robby Ginepri, below top form for much of this season, also had to fight hard before claiming his place in the last eight, outlasting Denmark's Kenneth Carlsen 7-6, 3-6, 6-4.
The American, who reached the semi-finals in Indianapolis last week before losing to Roddick, claimed his 11th victory in 28 matches this season.
GREAT SERVE
"I hung in there against Kenneth," the 23-year-old Ginepri told reporters. "He has a great serve."
The American took the first set on a tie-break but was outplayed by Carlsen in the second after being broken in the fourth game.
Ginepri appeared to hold the upper hand in the deciding set after breaking the Dane's serve for a second time to lead 4-1.
But both players then struggled to hold serve in a wildly fluctuating finish, the American being broken in the seventh and ninth games and the Dane in the eighth and 10th.
"Any time you can break after you just got broken, it's tough to do," said Ginepri, who will meet Slovakian Dominik Hrbaty in the quarter-finals. "I hung in there today."
In Thursday's opening match, seventh-seeded Hrbaty beat Germany's Lars Burgsmueller 7-5, 6-4.
The Slovakian broke his opponent's serve five times to reach his first ATP Tour quarter-final since advancing into the last four in Adelaide in January.
Eighth seed Tursunov charged into his fifth quarter-final of the year, beating 18-year-old Californian Sam Querrey 7-5, 6-4 in searing 114 degree heat at the Los Angeles Tennis Center.
The 23-year-old Russian, who climbed to a career-high 31st in the rankings last month, fired down 12 aces to set up a meeting with Roddick, should the top seed remain in the tournament.
