But Philadelphia refused to follow the script.
After the Sixers trailed 62-47, Green made two baskets to start a 10-0 run that sparked a comeback.
Miller gave Philadelphia a lead midway through the fourth quarter for the first time since late in the first.
After Chauncey Billups missed three of four free throws and a layup in 2-plus minutes late in the game, he made two from the line to pull the Pistons within one with 45 seconds left.
Detroit's Jason Maxiell drew a charge on the ensuing possession, giving the home team a chance to avoid an upset.
The Pistons set up a play that created an open shot for Tayshaun Prince, but his jumper was short. After Andre Iguodala made one of two free throws with 11 seconds left, Rasheed Wallace missed a shot near the basket that would have tied it at 88.
Iguodala then made two free throws with 7 seconds left to seal the win.
Wallace had 24 points, nine rebounds and matched a franchise playoff record with seven blocks.
Both teams will get two days off before Detroit hosts Game 2 on Wednesday night.
