Niese gave up three hits, struck out three and picked off a baserunner.
"I felt good," Niese said. "I think, for the most part, all of my pitches felt good."
Wright, playing in his final game before joining the U.S. for the World Baseball Classic, was 1 for 3 with a go-ahead RBI grounder.
"I feel ready," Wright said. "I feel as ready as a I can be after a week or so of games. I'm excited."
New York's Justin Turner had a two-run single in the sixth. Marlon Byrd had two hits and an RBI.
Prince Fielder had two hits for the Tigers, and Avisail Garcia hit a two-run homer in the fifth off Gonzalez German.
NOTES: Mets LHP Tim Byrdak arrived in camp Friday and will continue his rehabilitation from surgery to repair a torn anterior capsule in his shoulder. Byrdak hopes to be throwing off a mound by the end of spring training. ... Mets OF Lucas Duda saw a doctor for an undisclosed medical condition Friday and declared himself ready to play. Manager Terry Collins wasn't sure whether Duda will see action Saturday. ... Prior to the Friday's game, the Mets held a moment of silence for Sgt. Gary Morales, a St. Lucie County Sherriff's sergeant who was killed in the line of duty Thursday.