The Cavs, in their first Eastern Conference final since 1992, fell to 0-12 in Game 1s on the road.
For the fifth straight year, Detroit is among the NBA's final four and its experience seemed to help.
The Pistons didn't get thrown off when Cleveland got off to a good start and they made just enough shots and stops in the closing minutes to start the series with a victory.
"The second half was about will and determination," Wallace said. "They got everything they wanted in the first half, but in the second, we did what we had to do."
The Cavs led by as many as nine points in the first half and didn't trail in the game until Detroit started strong in the third quarter with a block and shot-clock violation on defense along with a 3-pointer and hook at the other end of the court.
The Pistons went on an 8-0 run to take a five-point lead and they led 56-55 entering the final quarter.
Detroit fell behind again in the fourth and didn't lead until Billups made a three-point play and a 3-pointer for a 71-68 lead with midway through the quarter.
Just when it seemed that the Pistons had control, the Cavs showed plenty of resolve in the back-and-forth quarter with an inspired effort that fell just short of their goal. Detroit beat Cleveland in seven games last year in the second round.
"It shows how much we've grown," Marshall said. "Last year in Game 1, we got beat by 20 or so in the same arena. Today, it came down to the last shot."