O'Neal looked remarkably sharp despite missing the Cavs' final 23 regular-season games after tearing a thumb ligament.
Derrick Rose had 28 points and 10 assists for Chicago, which trimmed a 22-point deficit in the third quarter to seven in the fourth.
But James converted a three-point play with 2:29 left and Mo Williams followed with a 3-pointer to put Cleveland up 94-81.
Williams added 19 points and 10 assists, and Antawn Jamison had 15 points and 10 rebounds. Cleveland blocked 12 shots - 10 in the second half.
Game 2 is Monday night in Cleveland.
Celtics 85, Heat 76
At Boston, Kevin Garnett had 15 points and nine rebounds and the Boston Celtics played Miami-style defense to beat the Heat.
Trailing 44-41 at halftime, the Celtics held the Heat to 32 points in the second half. And with substitute guard Tony Allen shadowing Dwyane Wade, the Heat star scored 26 points after averaging 33.7 in three regular-season games against Boston.
Allen also scored a career playoff high 14 points, and Paul Pierce led Boston with 16. Quentin Richardson added 15 for Miami.
Game 2 is Tuesday night in Boston.
Hawks 102, Bucks 92
At Atlanta, Joe Johnson scored 22 points, and Mike Bibby had 19 for Atlanta in Game 1 of the Eastern Conference series.
Jamal Crawford added 17 points for Atlanta in the first postseason appearance in his 10-year career. Rookie Brandon Jennings led Milwaukee with 34 points.
The Hawks had mismatches all over the court, taking advantage of the injury that took out Milwaukee center Andrew Bogut late in the season.
The home team never trailed, building a 20-point lead in the first quarter and going to halftime with a 62-40 edge.
Game 2 is Tuesday night in Atlanta.