Boston's win, which was the team's first in San Antonio since 2011, extended its seven-game winning streak and improved its league-best record to 7-1. Hayward tried to follow him, but his path was blocked by LaMarcus Aldridge, who stepped in with an illegal screen.
Hayward, who is in his third season with the Celtics and scored a career high-tying 39 points on Tuesday against Cleveland, told reporters he was exhausted of fielding questions about his health.
Kanter banged his knee in the second half of the Celtics' opening night loss to the Philadelphia 76ers and suffered a left knee contusion.More news: Barcelona held to a draw by Slavia Prague
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The 29-year-old left the game with nine points, two rebounds, one assist, one block and one steal.
DeMar DeRozan had 22 points for the Spurs (5-4), who trailed by as many as 22 points.
Two years removed from a devastating ankle injury that wiped out all but five minutes of his 2017-18 campaign, Hayward has enjoyed a return to his previous All-Star standard.