The Pacers fought their way into overtime when Paul George hit a 3-pointer with seven-tenths of a second remaining in the fourth period and George then hit three free throws with 2.2 seconds left in the extra period to put Indiana in front by one.
After a time out, James took a pass at the top of the key, spun around George and drove to the basket. Indiana's Sam Young, who had come into the game for 7-2 Roy Hibbert during the final time out, made no move to foul James and watched from under the basket as the winning shot went through the net.
After Miami had been off for a week and Indiana had been idle since last Saturday, the teams put on a riveting contest to start the conference finals. James posted a triple-double and the defending champion Heat overcame a combined 53 points from George and David West.
Miami will host the second game on Friday.
Neither side had more than a seven-point cushion during the entire game and the biggest advantage during the fourth quarter was Miami's 89-85 lead with 2 minutes to go.
Ray Allen had a chance to wrap up a Miami win in regulation, but he missed 1-of-2 free throws with 17 seconds remaining to leave the Heat in front by three.
George then came through with his game-tying, 3-pointer that was lofted over James.
A 3-point play by George with 2:10 to go in overtime gave Indiana a 99-96 lead, but Miami tied it on a 3-point play from Chris Bosh with 49 seconds to go at the end of a possession in which the Heat came up with two offensive rebounds.
James then gave Miami the lead on a layup with 10 seconds left, but Dwyane Wade fouled George while he was attempting a 3-pointer and when George made all three free throws it appeared Indiana might have pulled out a victory.
James ended that hope, however, by scoring the last of his 30 points. He also had 10 rebounds and 10 assists. Wade finished with 19 points and Bosh had 17.
George scored 27 points while hitting 10-of-11 from the foul line and West had five rebounds to go with his 26 points. Both sides had 20 turnovers.