Miller, who made six 3-pointers, went 33 for 62 (53.2 percent) from beyond the arc over Miami's last 10 games.
The Heat won despite playing without stars LeBron James, Dwyane Wade and Ray Allen, who were held out while recovering from injuries. The 33-year-old Miller, who is averaging 4.2 points, was 7 of 11 from beyond the 3-point arc and has a combined 56 points in the last three games.
Miller previously had of ear problems resulting from a head cold.
Miller reached the milestone with a 3-pointer with 10:25 left in the second quarter on Tuesday, when Miami hosted Oklahoma City in a rematch of last season's NBA Finals. Miller entered the game only one point shy of the mark. He's the second former Florida player to score 10,000 points, according to STATS LLC, and the 313th player in NBA history to reach that total.
He shot 7-for-8 from 3-point range in Game 5 of the NBA Finals last June, when the Heat clinched the title series over the Oklahoma City Thunder.
Miller was 7 for 8 from 3-point range in Game 5 of the NBA Finals against Oklahoma City, helping the Heat clinch the franchise's second championship.
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