Hamilton ended with a game-high 27 points, while Charlie Villanueva came off the bench for a double-double with 25 points and 11 rebounds to help Detroit bounce back from Wednesday's 103-90 loss to the Lakers.
"[Hamilton] had the juice and he had it flowing," said Pistons head coach John Kuester.
The Mavs, meanwhile, snapped a two-game skid of their own in Atlanta on Saturday when Dirk Nowitzki scored 21 points to lead five Mavericks in double- figures, as Dallas earned a 98-93 road victory over Atlanta.
Jason Terry added 15 points and seven assists off the bench for the Mavs, who survived a potential game-tying three from Joe Johnson in the final seconds to win in Atlanta for the second consecutive season. DeShawn Stevenson made all four of hits shots en route to 13 points, while Caron Butler also posted 13 points in the victory.
Shawn Marion recorded 12 points and 10 rebounds for Dallas.
"We did what we had to do. We got a big road win," Marion said. "We knew they were going to make a run. They're a talented team, and this is their home floor. Everybody played well for us. It was a great team win."
The Mavs have won four straight over Detroit and six of seven overall. The Pistons are winless in their last three trips to Big D.