Prince scored 23 points and Billups added 21, and the Pistons rallied from a 19-point deficit to beat the Chicago Bulls 81-74 on Thursday night in Game 3 of the Eastern Conference semifinals.
The Pistons, who swept Orlando in the first round, will try to wrap up this one Sunday at the United Center.
No NBA team has won a best-of-seven series after dropping the first three games, and only three major professional teams have done that - the 1942 Toronto Maple Leafs, 1975 New York Islanders and 2004 Boston Red Sox.
After blowing out the Bulls in the first two games at The Palace of Auburn Hills, the Pistons trailed 44-28 at halftime. They were down 49-30 early in the third and 55-38 midway through the quarter.
But Prince, Billups and Rasheed Wallace brought them back.
Prince scored 13 points in the third quarter and Billups added 10. Wallace had a block in the closing seconds and hit a 3-pointer at the buzzer to pull Detroit within 61-60. He then put them ahead with a jumper just under two minutes into the fourth and added a 3-pointer that made it a five-point game midway through the quarter.
Luol Deng led Chicago with 21 points, but was just 8-for-22 from the field. The Bulls were 28-of-83 (33.7 percent) almost the same percentage (33.6) they managed in the first two games.
They came up short at the free throw line as well, missing 10 in the game, seven of those in the fourth quarter.