Levine won for the sixth time in nine matches, and will face top-seeded Tommy Haas in the second round on Wednesday.
"I felt I played well," Levine said. "My first-serve percentage was pretty high and I was hitting the ball really good."
If he advances further, Levine could have a rematch with Marat Safin for the first time since beating him in the opening round at Wimbledon.
Levine said he ran into Safin on Sunday and often-mercurial Russian "just said hi. I was a little nervous about because he's three times as big as me, but he just said hi."
Safin, the No. 8 seed in this 28-player field that is void of any top 20 players, beat Pete Sampras later Monday night in an exhibition rematch of their 2000 U.S. Open final, which Safin won.
Safin won the exhibition 10-6 in a tiebreaker after they had split two sets. The Russian had said he wanted the match to be "all about fun. It's not about to show to each other who is the best one and whatever. I know he was much better player than me."
Sampras, who won this tournament twice, said he'd like to play an exhibition or a Seniors Tour match every three or four months, but he hoped it wouldn't come as a surprise to anyone that "I'm not quite as good as I used to be."
The crowd didn't seem to mind at all, cheering and groaning at all the appropriate moments during the fast-paced match.
Levine, a 5-foot-9, 150-pound left-hander who likes playing on grass, came out of qualifying to beat Safin in four sets and went on to lose in the round of 32 at Wimbledon and said he "took some confidence" from that event. He followed that by reaching the quarterfinals on grass at Newport, R.I., and lost in the second round after qualifying at Indianapolis.