Levi, who won here in 1990, did not make a bogey, a distinction matched by Johnson, who has missed the cut in 10 of 16 events this year.
John Daly made his return to the PGA Tour after a five-week absence and scored a one-over 71. The former PGA and Open champion was playing for the first time since withdrawing from last month's US Open citing difficulties stemming from his alcoholism treatment.
"I didn't mishit too many shots today, plus I had some good up-and-downs," said Johnson, who qualified for the Tour by finishing 10th on the 1996 Nike Tour money list. "It was the most solid ball-striking round I've had."
Levi's victory here in 1990 was one of four triumphs he enjoyed in 1990 on his way to Player of the Year honours. He has not won a tournament since. "I never got in any trouble," Levi said. "When you don't make mistakes, you can score well. I've been playing OK. I'm not working as hard on my game as I used to."