On a day when nine hours of play were lost to rain, the third seed and 2005 champion advanced at his home tournament as he stretched his perfect record against Clement to seven wins out of seven.
Blake, runner-up to world number one Roger Federer in the Cincinnati Masters last week, will play 16th seed Agustin Calleri of Argentina or unseeded American Robby Ginepri in the third round.
"I think I am playing some of my best tennis," Blake said.
"American hard courts is where I feel the most comfortable. It suits my game the best, I've got the fans on my side and I end up feeling great.
"I feel like I am playing better than when I won here in 2005 but the tour is getting better as well."
In the women's event, Indian Sania Mirza advanced to the second round with a 6-3 6-3 win over Spaniard Anabel Medina Garrigues.
Also see: Images: Sania's opening match interrupted by rain
In the day's other men's match, American wildcard John Isner continued his superb start to his professional career with a 6-3 6-4
In just his fourth ATP event, the 6ft, 9ins Isner, who reached the final in Washington earlier this month, banged down 13 aces to hand Becker his sixth straight defeat.
LOSING BET
Isner, who has climbed from 839 in the rankings to 199 in just two months, will play fourth seed David Ferrer of Spain in the second round.
The 22-year-old arrived at his post-match press conference wearing a James Blake T-shirt, the result, he said, of coming out on the wrong side of a bet with his compatriot before the tournament.
"I have to wear this after every match this week," he said.
"It wasn't really a bet but he helped me out, to get into this tournament, so I said I would do anything I could.
"In the warm-up, I have to wear this Nike shirt that he autographed, and it's awful."
Blake said he was enjoying having some fun with Isner.
"It's fun to be hazing someone who is about 10 inches taller than me," he said.
"He's a great kid. He has got a ton of potential. In tennis years, he is very young, so the success he's having at this level is incredible."
