James finished with 28 points, 10 rebounds and eight assists in Miami's third straight win. The Heat remain unbeaten at home in five outings, the first time in franchise history the team has won its first five home games.
After James tied it at 98-98, both Monta Ellis and John Henson missed jumpers for Milwaukee.
Dwyane Wade then hit the opening field goal of the extra period and James soon followed with two more. Wade, returning from a two-game absence, also scored 28 points, while Chris Bosh had 24 points and 18 rebounds.
Brandon Jennings led Milwaukee with 19 points, seven rebounds and six assists. Rookie John Henson contributed 17 points and 18 boards.
The Bucks have lost two in a row after having won six of their first eight.