The Spurs point guard briefly left the game as the Heat went on to win Game 2.
Parker looked to be ailing even after returning to the game, and San Antonio fell to the Heat 98-96.
The foul occurred with 6:43 remaining in the fourth quarter, with the Spurs holding on to a two-point lead. The Spurs missed four consecutive free throws resulting from the foul, and never looked the same from then on.
San Antonio head coach Gregg Popovich bemoaned his team's sloppy offense and the mistakes that plagued them in the fourth quarter.
"LeBron with the ball did a pretty good job at his end and we had to be really perfect at the other end and we didn't," Popovich said. "We didn't take advantage of things. We made bad decisions."
The Spurs will need Parker and their offense to be firing on all cylinders if they are to take one of the next two games in Miami.