Young won the National League stolen base crown with 46 and helped the Mets rally past Milwaukee 3-2 on Sunday when the Brewers botched two bunts in the eighth inning.
"I just talked to him before I walked in here. He's about as high as you can get," New York manager Terry Collins said. "That's a great honor for him."
The speedy Young swiped two bases in the first, scored on a shallow sacrifice fly and later threw out a runner at the plate from left field. He began the day tied for the NL lead in steals with Milwaukee shortstop Jean Segura, who sat out for the 10th time in 11 games.
Segura returned Saturday from a strained right hamstring, but he and the Brewers didn't want to push it in the season finale, manager Ron Roenicke said.
"Now after it's all said and done, it's a great feeling that I was able to do it. Like I said, I'm glad we finished the season on a winning note," said Young, acquired from Colorado in June. "I'm proud of myself. That's my craft, stolen bases, and you always pride yourself in what your craft is."
Young's father led the NL in stolen bases with 53 for the Rockies in 1996.
Playing in front of their third sellout this season, the injury-riddled Mets prevented a four-game sweep by Milwaukee and finished 74-88 for the second consecutive year. They have endured five straight losing seasons since moving into Citi Field.
New York did make a bit of progress with a third-place finish in the NL East, its highest since second in 2008. The Mets had come in fourth for four consecutive years.
Before the game, former slugger Mike Piazza was inducted into the team's Hall of Fame during a 30-minute ceremony on the field.
After the final out, Young applauded as Mets players tossed their caps into the stands behind the dugout.
"Very nice. It's indicative of the way we've gone about things: Battling, battling, battling -- battling again today to come away with a win," Collins said. "I'm very proud of them. It's a good way to end the season."
Marco Estrada allowed two hits in seven sharp innings for the Brewers, who finished 74-88 for fourth place in the NL Central. They had won four games in a row and 12 of 17.
Estrada struck out eight and walked none.
"Marco threw the ball outstanding," Roenicke said. "He pitched well enough to earn a shutout."
Milwaukee scored twice on five singles and a walk in the fourth, then carried a 2-1 lead into the eighth. Lagares reached on a throwing error by shortstop Jeff Bianchi, and Juan Centeno dropped down a bunt in front of home plate.
Second baseman Scooter Gennett was late covering first and bumped into umpire CB Bucknor while trying to navigate his way toward the bag. The low throw from catcher Jonathan Lucroy skipped up the right field line for an error that allowed Lagares to score all the way from first.
One out later, Young drove in the go-ahead run with a dribbler to reliever Brandon Kintzler (3-3).
"My gosh, not the way you want to end a season," Roenicke said.
Milwaukee CF Carlos Gomez stole a base to become the first Brewers player with 20 homers and 40 steals in one season. ... Brewers starters had a 2.94 ERA in September. ... Young scored on David Wright's short sacrifice fly in the first inning after stealing second and third. ... The only other Mets player to lead the league in steals was Jose Reyes, who did it from 2005-07. ... Lagares finished with 15 assists, a Mets record for rookies and the most by a rookie outfielder in the majors since Delmon Young had 16 for Tampa Bay in 2007. ... New York 2B Daniel Murphy ended the season with an 11-game hitting streak. He also had 22 consecutive stolen bases, the second-best streak in club history. ... The Mets finished 33-48 at home. Only the Chicago Cubs (31-50) were worse in the NL. ... New York went 2 for 32 (.063) with runners in scoring position during the series. ... Mets home attendance has dropped in five straight seasons for the first time in franchise history. With the crowd of 41,891 for the finale, the Mets drew 2,135,657 this year for their lowest home attendance since 1.77 million at Shea Stadium in 1997.