Chris Bosh scored 13 points and James Jones had 12 for the Heat. Game 2 of the best-of-seven series is Wednesday.
Kemba Walker scored 20 points for the Bobcats, who led by nine early and led again in the third. Al Jefferson missed eight of his final 13 shots after getting hurt in the first quarter. He finished with 18 points and 10 rebounds for the Bobcats, who got 17 from Gary Neal and 15 from Josh McRoberts.
Miami sealed it with an 18-4 run in the fourth, all but three of those points coming with James getting a rest.
SPURS 90, MAVERICKS 85
SAN ANTONIO (AP) — Tim Duncan scored 27 points, and San Antonio held Dallas to one field goal in the final seven minutes to win Game 1 of their first-round playoff series.
The Mavericks also went scoreless for 5½ minutes during that stretch, their lone field goal coming as time expired.
Tony Parker had 21 points, and Manu Ginobili added 17. Kawhi Leonard had 11 points and 10 rebounds and Tiago Splitter pulled down 11 rebounds for top-seeded San Antonio, which has won 10 straight against Dallas.
Devin Harris scored 19 points for the Mavericks, who nearly pulled off a huge upset.