Losing for the 12th time in the last 14 games, the Jazz never figured out how to stop Drummond or Monroe, a pair of 6-foot-11 post players who dominated around the basket.
Drummond finished with 19 points and 14 rebounds. He went 9-for-10 from the field.
Monroe contributed 18 points and 11 rebounds. He made nine of his 15 field-goal attempts.
"They're both good players," said Jazz center Derrick Favors, "and they both had very good games."
In the opening three minutes, Drummond scored four points and Monroe added a 15-footer as Detroit raced to a 9-2 lead.
"We had a really nice start and I think that set the tone," said interim coach John Loyer.
Said Favors: "They were being aggressive and making a lot of tough shots. We missed a lot of shots we normally make including myself and I think that affected our defense."
Asked about the Pistons' ability to dominate the paint, Jazz coach Tyrone Corbin shook his head.
"I thought we would be a little better," he said. "Give their guys credit. Drummond was good in there and Monroe pounded and was able to get some shots in there. ... [But] we didn't do a good job of taking that away. They got a lot of paint touches too much of what they wanted."
During the Jazz's 110-89 win at the Palace of Auburn Hills in January, Monroe finished with four points and one rebound. He made only one of his seven shots.
Drummond was a little better, but his 10 points and 13 rebounds did not impact the game like his performance in the rematch.
"When you see the ball go in the hole," Corbin said, "your confidence goes up. I thought that's what happened with their whole team tonight."
Piston prolific in paint
• Detroit big men Andre Drummond and Greg Monroe combine for 37 points and 25 rebounds in a 114-94 win over Utah.
• Drummond and Monroe scored six points during a game-opening 9-2 run that put the Pistons in control from the start.