Playing the first match on a sun-drenched Centre Court, Roddick hit 25 aces, lost serve just once, and committed only 11 unforced errors.
"That was as tough a second round as there is," Roddick said.
Seeded fifth, Roddick struggled early trying to read Llodra's serve. He broke for the first time at love in the final game of the second set to even the match, then won five consecutive games in the third set to take control.
Roddick began playing serve and volley more as the match progressed, and he won 34 points at the net.
"I had to make an adjustment," Roddick said. "Off my serve, I had to start coming in and serving and volleying behind it."
Five-time Wimbledon champion Venus Williams lost only 11 points on her serve and beat Ekaterina Makarova 6-0, 6-4. Williams is seeded second behind her sister Serena, who won when they met in last year's final.
Justine Henin was also made to sweat during her second-round match. The seven-time Grand Slam champion twice was broken serving for the victory, then regrouped and beat Kristina Barrois 6-3, 7-5.
Fellow Belgian Kim Clijsters also advanced, beating Karolina Sprem 6-3, 6-2. Clijsters and Henin are both back at Wimbledon after coming out of retirement, and they could meet in the fourth round.
No. 13 Shahar Peer lost to Angelique Kerber 3-6, 6-3, 6-4. No. 11 Marion Bartoli advanced with a walkover against Petra Martic.
Umbrellas were out _ not for rain, but as shields from the sun on the hottest day of the tournament.
With temperatures heading into the low 80s, the All England Club's public address announcer advised spectators to make sure they had skin protection, head wear and water. Williams rubbed a cold water bottle across her face during a changeover.
"All are vital necessities," he said.
No. 15 Lleyton Hewitt, the 2002 champion, advanced when Evgeny Korolev retired trailing 6-4, 6-4, 3-0. American Mardy Fish served 30 aces but missed all nine of his break-point chances in the final set and lost to Florian Mayer 6-7 (2), 6-3, 6-4, 6-4.
Roddick won his only Grand Slam title with an overpowering serve and forehand at the 2003 U.S. Open, and he's now a much different player, using a wide variety of shots. He showed the broad repertoire down the stretch against Llodra, feathering a slice forehand for one key winner, hitting a loopy topspin forehand for another and dropping a pinpoint lob in the corner to take the lead for good in the tiebreaker.
"He played an almost perfect first set," Roddick said. "It took some of my best stuff today to get through that. I thought I played really well. I think I had to."
Henin built leads of 4-1 in the first set and 5-1 in the second. Serving for the win at 5-2, she double-faulted on consecutive points and lost the game, then lost serve again for 5-all.
But Henin broke back and served out the victory at love. She exhaled in relief after winning the final point against the German.
"I was sometimes too much in a rush to finish, probably because she gave up at that time and my intensity really dropped down," Henin said. "I had a good reaction to the situation."
Henin won 21 points at the net and hit 38 winners. She seeks the only major title she has yet to win.
"That remains a dream for me," she said. "I just see myself as an outsider this year, because I don't know how I'm going to deal at a very high level. So it's very hard to predict what could happen, but I really don't see myself as one of the favorites."
Seeded 17th, the Belgian is playing at Wimbledon for the first time since 2007. She retired in 2008 and rejoined the tour in January.
Clijsters committed just 13 unforced errors against Sprem and erased the only three break points she faced. The No. 8-seeded Clijsters, who returned from retirement last year, is playing at Wimbledon for the first time since 2006.
She has reached at least the third round at her past 16 Grand Slam tournaments.