Sidelined by cramp late in the series opener, James responded by scoring 35 points in game two at the AT&T Center.
He also pulled down 10 rebounds and provided three assists as the Heat squared the series at 1-1 and took home-court advantage off the Spurs.
The two-time defending champions head to their American Airlines Arena home in Florida for games three and four on Tuesday and Thursday respectively.
The Heat have now won 13 straight post-season games following a play-off loss.
Chris Bosh (18 points), Dwyane Wade (14) and Rashard Lewis (14) were good contributors, with the latter making three three-pointers.
For the Spurs, Tony Parker had 21 points and seven assists, while Tim Duncan finished with a double-double of 18 points and 15 rebounds.
Manu Ginobili contributed 19 points, while Boris Diaw had 10 rebounds.
The opening quarter belonged to the Spurs and Duncan, who made 11 of their 26 points as they led by seven.
Miami were level at half-time and it was close throughout the second half, with the Heat taking a two-point lead when Bosh made a three-pointer with 78 seconds remaining.
A Ginobili turnover led to the Heat going three ahead when James made one of his two free-throws.
A Wade lay-up extended their lead to five and there was no way back for the Spurs despite Ginobili hitting a three on the buzzer.
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