Greek playmaker Antetokounmpo scored 50 points, grabbed 14 rebounds and added six assists to rally the Bucks over the visiting Utah Jazz 122-118, AFP reported.
The reigning NBA Most Valuable Player's run of 17 double-doubles to start a season is the NBA's longest since 1976.
"I'm just trying to get better," said Antetokounmpo.
"Take it day by day, game by game and just get myself ready in games that matter the most.
"We want to be the last team playing at the end of the season."
Four-time NBA MVP James scored 33 points and passed off 14 assists while Anthony Davis contributed 19 points and 12 rebounds to spark the NBA-leading Lakers in a 114-104 victory at San Antonio.
"He was unbelievable," Lakers coach Frank Vogel said of James.
"He just dominated the action, made everything offensively."
The Lakers improved to an NBA-best 15-2 to pace the Western Conference with Milwaukee atop the Eastern Conference at 14-3, the league's second-best record.
"It's good to be in the position we're in," James said.
James made 13-of-24 shots from the floor, including 4-of-7 from three-point range, and his 12 in the fourth quarter helped the Lakers improve to 7-1 on the road.
"I just want to be able to not have any weaknesses and allow a defense to dictate what I do," James said.
"Just trying to be the most complete basketball player I can be."
The Bucks are on their longest win streak since the 2001-02 season.
"We're just playing together and having fun," Antetokounmpo said.
"Our defense has been really good lately."
Antetokounmpo scored 32 points in the second half to spark a comeback for the Bucks and chants of "M-V-P" from Bucks fans.
Utah led 57-48 at half-time but surrendered 42 points to Milwaukee in the third quarter and made only 26.
Utah's Donovan Mitchell was driving for a tying layup in the dying seconds but Brook Lopez blocked the shot to preserve Milwaukee's victory.
"It was a big-time block," Antetokounmpo said.