Gleyber Torres also drove in three runs as the Yankees won for the sixth time in seven games and improved to 13-14.
But the headliner was Taillon (1-2), who allowed one run, three hits and struck out eight over five innings. The Yankees had lost in each of his four previous starts.
Taillon's previous win came on May 1, 2019, for Pittsburgh in his last outing before having Tommy John surgery. The Pirates traded him to the Yankees before this season.
"He was player of the game for us today, for sure," Judge said of Taillon. "It was a special moment. Whenever you have a big injury like that, Tommy John, you know some players might think it's over. But for him, it's work, work, work, and I'm really impressed."
"To me, he's an inspiration," he said.
Taillon, who called the effort "a step in the right direction," retired seven straight hitters before Jeimer Candelario's two-out homer in the fourth tied it at 1. Taillon issued consecutive two-out walks in the fifth but escaped unscathed by striking out Miguel Cabrera.
"It means a lot to him. He loves being here, and I'm sure it was emotional for him," Yankees manager Aaron Boone said. "Knowing that it was two years, I'm really excited for him. Everyone has been through stuff, and Jamo has definitely been through his trials.
"It was another step forward for him."
Taillon got an unlikely assist in the fifth inning with Detroit threatening to take the lead when Niko Goodrum attempted to advance to third on JaCoby Jones' hard-hit grounder to the left side of the infield. The ball took a hard bounce, however, and struck Goodrum in the leg for the second out of the inning. Jones was credited with a hit.
"It took me a little longer than I would have liked," Taillon said of not winning a game until May. "There were times where I wasn't 100 percent sure I'd ever be in a major league uniform again, let alone pitching for a team like the Yankees."
In a big league season in which hitting is in short supply, 11 of the 18 batters in the starting lineups for the Tigers and Yankees finished the game hitting .198 or below. Detroit began the day with a majors-worst .199 team batting average, and Cabrera, a former Triple Crown winner, went 0-for-5 and fell to .125, one of the five Tigers under .200. But the Yankees, slowly coming around on offense after an inconsistent open to the season, had enough to support Taillon's effort.
"My awareness to situations today was a little better," Taillon said. "To start the year, there's been some ups and some downs, but I've learned a lot."
His manager agreed.
"He's continuing to pound the strike zone, executing at the top of the strike zone with his fastball," Boone said. "Today was another day of that, knowing that he's been through a lot to get to this point."
Spencer Turnbull (1-2) gave up four runs and five hits in five innings. The Tigers lost their fourth in a row and dropped to an MLB-worst 8-20.
Judge followed Friday night's two-homer, five-RBI performance by breaking a 1-all tie in the fifth inning with a line-drive double off Turnbull to left field that scored DJ LeMahieu.
Turnbull lost control in the sixth inning when he hit Aaron Hicks to open the frame and then walked Gary Sanchez and Clint Frazier before reliever Jose Cisnero replaced him, as the Yankees moved to within one game of the .500 mark.
"We want to definitely be way over .500," Judge said. "We just have to keep having that mindset, that every game is the first game of the year."
New York's Aroldis Chapman pitched a perfect ninth for his fifth save in as many chances.
The Associated Press contributed to this report.