Monta Ellis had 21 points and 11 assists for Milwaukee. Brandon Jennings added 14 points and Ersan Ilyasova scored all of his 17 points in the first half.
San Antonio outrebounded Milwaukee 53-36, including a 28-17 advantage in the second half.
The Spurs opened the game by missing their first 11 attempts before Parker banked in a runner with eight minutes left in the opening quarter. The Spurs offset that poor shooting with 11 rebounds.
Ilyasova scored eight straight points for the Bucks in a two-minute span late in the first quarter, besting his season average of 6.9.
"In the first half, we were sharing the ball more," Ilyasova said, "getting open looks and knocking them down. In the second half, they played better defense."
Every active Spurs player with the exception of James Anderson scored for San Antonio, which needed the balanced scoring with Green, Stephen Jackson, Kawhi Leonard and Patty Mills all sitting out with injuries.
Notes: San Antonio recalled G Cory Joseph and G De Colo after assigning both to the team's NBDL team in Austin to get some playing time. De Colo was assigned to the Toros on Sunday, scored 14 points in 39 minutes that night and was recalled Monday. . San Antonio hosts Houston on Friday before opening a four-game road trip Saturday in Charlotte. The Spurs have three road trips of at least four games in the first 45 days of their season. Their nine road wins are the most by any team in the NBA this season. Oklahoma City is second with six.