SAN ANTONIO -- Despite little, if any, contribution from ailing team leader Giannis Antetokounmpo, Milwaukee found itself within striking range of the San Antonio Spurs in the final minute on Tuesday and the ball in the hands of the Michael Beasley, one of the league's streakiest players.

But the Spurs double-teamed Beasley, who had torched them for a season-high 28 points, and he passed out of the pressure defense to rookie guard Malcolm Brogdon in the far corner. Brogdon calmly hit the go-ahead 3-pointer with 1:08 to play and added a free throw in the final seconds as the Bucks stunned San Antonio 109-107 at the AT&T Center.

Beasley tied the game at 101 at the 3:22 mark on a driving layup and after a poor shot by the Spurs' Kawhi Leonard, Jabari Parker's layup gave the Bucks a 103-101 lead with 2:56 to play in regulation.

Two free throws by Beasley pushed Milwaukee's advantage to 105-101 but Spurs reserve forward Davis Bertans cut the lead to one point with a ringing 3-pointer and Danny Green put San Antonio back in front with a catch-and-shoot 3-pointer at the 1:20 mark.

Brogdon calmly canned his deciding 3-pointer on the following possession. A Bertans 3-pointer from above the top of the key with 10.9 second to play rimmed out and was rebounded by Jabari Parker.

Brogdon then hit 1 of 2 free throws with 7.1 remaining but left the door open for a final San Antonio shot to tie or win. The Spurs got the ball in the corner to Manu Ginobili with 1 second to play, but his 3-point-attempt hit the side of the backboard and bounced away.

"Beasley was the heart and soul for us tonight, and we leaned on him and he came through for us," Brogdon said. "He is a huge calming factor; he's never too high or too low and he had an aggressive mentality. Being the honey and attracting everybody while kicking the ball out was great. He passes almost as well as he scores."

Jabari Parker added 22 points while Brogdon had 17 and Greg Monroe added 14 for Milwaukee (19-18), which snapped a nine-game losing streak to San Antonio.

The Spurs got a game-high 30 points from Leonard, his ninth 30-point game this season, and 14 points each from Tony Parker, Danny Green and Jonathan Simmons. Bertans added 11 and David Lee scored 10 points for San Antonio (30-8), which had a three-game win streak snapped.

The Spurs played without LaMarcus Aldridge, who was out with a stomach illness, while Antetokounmpo played nine minutes but did not score after missing Milwaukee's previous game Sunday with an illness.

"The problem was that we didn't guard very well," Spurs coach Gregg Popovich said. "Obviously Beasley was great -- we never stopped him. But in general of defense was not up to par and they took advantage of it and did a great job offensively."

San Antonio led by many as eight points in a back-and-forth first quarter that ended tied at 23. Jabari Parker hit for 11 points in the period for Milwaukee and was the only Bucks' starter to score while all five Spurs' starters scored at least two points.

San Antonio picked up the pace in the first three minutes of the second quarter, using a 13-2 run to build a 36-25 lead. Leonard had 11 points in the surge, pouring in back-to-back 3-pointers before adding a pair of midrange jumpers.

Tony Parker scored eight straight points for the Spurs in a minute and a half stretch at the end of the quarter to take a 59-46 lead, but the Bucks responded by scoring the final seven points of the half that included a layup by Jabari Parker and three free throws by Brogdon after a foul by Leonard with 0.9 second to play. San Antonio settled for a 59-53 advantage at intermission.

"At the end of the game they hit a couple of tough shots that were contested and we missed a few that were wide open," Lee said. "We had a couple of stretches when we didn't play our best defense. At the end of the second quarter we had a chance to go into the locker room up 10 or 11 but the three free throws there cut the lead to six and gave Milwaukee some bounce in their step."

Leonard led the Spurs with 16 points in the half while Tony Parker added 10 for San Antonio. That offensive putout was equaled by Jabari Parker's 16 for the Bucks and Brogdon's 10 points.

Milwaukee crept closer in the third quarter, cutting the Spurs' lead to 84-81 on layup by Monroe with 45.7 seconds remaining. An alley-oop dunk by the Spurs' Dewayne Dedmon was followed by two free throws by Beasley that again reduced the San Antonio advantage to three points, but Ginobili poured in a 3-pointer with 2.5 seconds left in the period to allow the Spurs an 89-83 lead heading into the fourth quarter.

San Antonio led 97-94 with 5:02 to play before Leonard hit a contested baseline jumper, was fouled by Beasley and hit the ensuing free throw to expand the advantage to six points.

Beasley said his performance was just part of the Bucks' next-man-up focus.

"I was doing what our coach allowed me to do -- our big dog was down tonight and we needed someone to step up," Beasley said. "I was just taking what they gave me -- just playing basketball the right way and having fun and making the right decisions.

NOTES: On March 6, 1982, San Antonio beat Milwaukee 171-166 in triple overtime in the HemisFair Arena. The Spurs' point total in that game is a club record and the combined point total of 337 is the second highest recorded in NBA history. ... Milwaukee won two of the past 15 meetings. The Bucks' previous win against the Spurs came Jan. 10, 2012 in a 106-103 victory in Milwaukee. That game was one of only two in Bucks' history in which they won despite allowing their opponent to shoot at least 60 percent. ... Bucks assistant coach Joe Prunty began his NBA coaching career in San Antonio. He was on the Spurs' staff for nine seasons from 1996-97 to 2004-05 and was a part of San Antonio's championship teams in 1999, 2003 and 2005.