Chalmers finished with 19 points, and James had 17 points, eight rebounds, seven assists and three blocks — the best on Tiago Splitter's dunk attempt — while shooting only 7 of 17 from the field.
"Honestly, for me, when I was struggling offensively, my teammates continued to keep it in range," James said. " And we even had a lead at one point, especially late in the second quarter when we made that run and I was struggling a little bit.
"So I think Rio more than anybody kept us aggressive, him getting into the paint, him getting those and-ones and making a couple of 3s. It allowed me to sit back and wait for my time."
The Heat made 10 of 19 3-pointers and got 13 points from Ray Allen, and 12 points and 10 rebounds from the previously slumping Chris Bosh.
Danny Green made all six shots, including five 3-pointers, and scored 17 points for the Spurs. They host Game 3 on Tuesday night.
Parker had 13 points on 5-of-14 shooting for the Spurs, who were so precise in their 92-88 victory in Game 1 but threw the ball all over the white-surrounded court Sunday, committing 17 turnovers that led to 19 Miami points.
"In the second half they just run us over," the Spurs' Manu Ginobili said. "We didn't move the ball at all. Their pressure really got us on our heels."
Tim Duncan shot 3 of 13 and finished with nine points and 11 rebounds.
"We didn't play well. We didn't shoot well. I know I played awfully," Duncan said. "Whatever it may be, they responded better than us. So hopefully we can look forward to this Game 3 and regain some of our composure."
James insisted he wouldn't force himself to do more after he had a triple-double in Game 1 but never seized the opportunity to take control of the scoring as the game was slipping away from the Heat.