In the second set, Isner fell behind 0-15 in the eighth and 10th games, then reeled off four straight aces in both games to hold onto his serve. But Levine won the final two games of the second set to force a decisive third set.
Levine lost serve in the first game of the third set to set Isner up for the win.
"It was a long one and good one to get through," said the 15th-ranked Isner, who had 28 aces in the match. "I anticipate I'll get better going forward.
"But a wins a win and I haven't had many recently and I'm just trying to get this train going."
Fourth seeded Kei Nishikori, who won last week's Memphis title, retired with a back injury against 150th-ranked Ivo Karlovic of Croatia. Karlovic was leading 5-4 in the first set when Japan's best player abandoned the match.
Seventh-seeded Feliciano Lopez of Spain, who lost to Nishikori in the Memphis final, pulled out of the tournament today with a left wrist injury.
Nishikori became the third player to retire from first-round matches at Delray this week.
Earlier in the day, second-seeded Tommy Haas of Germany moved into the second round when Igor Sijsling of the Netherlands retired with an injured left ankle after the two split sets. Sijsling won the first 7-5, Haas the second 6-4.
A frustrated Sijsling belted three balls into the stands, hitting a spectator with one of the balls. He received a code violation warning, lost his serve which evened the score at one set apiece, and retired from the match.
"What a strange match," Haas said. "At 4-all, first point, I saw him falling to the ground. Sometimes you don't know how to react when someone is injured, but he looked like he was in pain.
"The first couple of points went my way and he started to smash balls out of the stadium and hit a spectator. You never want to win a match like that. It's not a proud win for me."
Ryan Harrison lost to qualifier Daniel Munoz-De La Nava of Spain 6-2, 1-6, 6-3, squandering a 3-1 lead in the final set. Jack Sock, a wildcard into the main draw, beat Mathew Ebden of Australia 6-3, 6-3.