MILWAUKEE -- Saturday night, the Milwaukee Bucks were as close to full strength as they've been all season and it turned out, they'd need every bit of it to outlast the Cleveland Cavaliers, 108-105 in double overtime at the Bradley Center.

Milwaukee led for most of the second and third quarters and had plenty of chances to put the game away early in the fourth, but when the Bucks' shots stopped falling, Cavaliers forward LeBron James took over.

James scored a game-high 37 points and accounted for Cleveland's final six points of regulation. He tied the game at 94-94 on a drive through the lane for an easy dunk with 16.5 seconds left.

"You're going to give up something and we didn't want to give up a 3 at that point," Bucks coach Jason Kidd said. "Being the basketball player he is, he saw it, took advantage of it and made a drive to the basket to lay it in."

Milwaukee had a chance to win at the buzzer but reserve guard Jerryd Bayless' jumper was short, and the teams moved to overtime.

Again, James was a dominant force for the Cavs, dropping in seven points during the first extra session. But with a chance to win it at the buzzer, James passed up on a drive and settled for a long 2-pointer that missed.

He'd add four more in the second extra session, but Milwaukee got 3-pointers from forward Giannis Antetokounmpo and guard Greivis Vasquez, and went 6-for-6 from the free-throw line to close it out.

"We played from behind and I've tried to get us out of a hole late," James said. "Maybe I need to get (my teammates) involved earlier."

Bayless had 17 off the bench to lead Milwaukee and also grabbed six rebounds to go along with five assists. To top it off, he spent the game's final minutes matched up against James after Antetokounmpo fouled out.

"Go guard him," Bayless said. "That's all it was, nothing else. As great as he is, I'm going to try to make it as tough as possible for him. That was my mentality going into it."

Point guard Michael Carter-Williams also finished with 17 points while Antetokounmpo and center Greg Monroe added 16 each -- with 11 and 17 rebounds, respectively -- and forward Jabari Parker had 12.

"We just have to take what we did in this game, the intensity and the energy we played with, and carry it over," Monroe said.

Forward Kevin Love added 24 with 14 rebounds for Cleveland, which shot 40.7 percent from the field and was 14-for-38 from beyond the arc.

The Cavaliers also committed 21 turnovers, which Milwaukee turned into 26 points.

"We have to do a better job," said James, who had seven turnovers on the night. "Myself included."

Milwaukee wiped out an eight-point deficit with a 13-2 run to go up 42-39 with 4:29 left in the first half. Love's 3-pointer tied the game with 4:13 remaining, but the Cavaliers wouldn't get another field goal the rest of the way and Carter-Williams' tip-in at the buzzer sent Milwaukee into halftime up six.

The lead grew to nine by the end of the third but seven straight points from forward Richard Jefferson, who hit a pair of 3-pointers, made it a two-point game with 10 minutes to play.

Milwaukee recovered quickly, ripping off a 9-2 run that created breathing room before James took over down the stretch.

"This is the best team in the East and one of the best in the league," Kidd said. "We had opportunities to win it but we kept playing, kept competing."

NOTES: PG Michael Carter-Williams returned to Milwaukee's starting lineup and played 40 minutes after missing five games with a left ankle injury. His return gave the Bucks their full starting lineup for the first time this season. ... The Bucks were without PG Tyler Ennis and SG O.J. Mayo, who hasn't played this season because of a hamstring injury. ... Cleveland SF Richard Jefferson was available, one day after suffering an ankle injury Friday night in New York. ... Bucks F Giannis Antetokounmpo began the day third in the NBA with 3.9 fouls per game. ... Cavaliers SG J.R. Smith went 4-for-14 from the field and 2-for-8 from beyond the arc. He came into the game shooting just 25 percent (4-for-16) on 3-point attempts this season, well behind his career rate of 37.1 percent.