Omar Quintanilla drew a one-out walk before right-hander Luis Mendoza got the second out, but Young hammered a 3-1 pitch over the right-field fence for a walk-off win.
"I knew it I hit it hard. I really don't worry about the dimensions of the field," Young said. "Q was running as soon as I hit it. I was looking for a line drive in that situation. Thankfully, it got up."
For the first time in 10 games, the Royals were watching someone else celebrate a victory.
"It was a hard-fought game. We had opportunities to push runs across, especially late, to get Holly [closer Greg Holland] in the game, but we just couldn't do it," Royals manager Ned Yost said.
Mendoza, normally a long reliever, was brought into the game in the 10th inning because Tim Collins and Luke Hochevar weren't available out of the bullpen.
"He was the last guy I had," Yost said.
Collins was not with the team because he was with his ailing grandfather, but he's expected to rejoin his teammates on Saturday. Hochevar was unavailable after throwing two innings in Thursday's win.
In the 10th, the Mets got the first two runners on base against Mendoza, but he escaped the jam by getting ex-Royal John Buck to rap into an inning-ending double play. In the 11th, with Quintanilla on base, Mendoza threw three balls to Young. After a strike, Young sent the next pitch soaring.
"A home run, that's all," Mendoza said in the quiet visitors' clubhouse.
The Mets took a 2-1 lead into the ninth inning, but the Royals didn't let it end there.
Mets closer Bobby Parnell has a stiff neck, so right-hander David Aardsma was called on to pitch the ninth. Pinch-hitter Miguel Tejada led off with a double to left-center field and Alcides Escobar walked. Elliot Johnson put down a perfect sacrifice bunt to advance the runners. Billy Butler was sent out to pinch-hit for Jarrod Dyson, and the Mets intentionally walked him to load the bases.
"We got in a situation where we knew they were probably going to walk Billy, but we had to put Elliot in that situation to get the runners in scoring position," Yost said.
He still had Lorenzo Cain and Alex Gordon coming up next.
Cain hit a long sacrifice fly to center field, with Tejada jogging home to tie the game at 2. Left-hander Pedro Feliciano relieved Aardsma and got Gordon to bounce out.
The drama continued in the Mets' half of the ninth against reliever Aaron Crow.
Ike Davis led off with a double down the right-field line. Pinch-runner Andrew Brown was bunted to third by Quintanilla, but pinch-hitter Justin Turner struck out. Young was intentionally walked and Juan Lagares grounded out to send the game into extra innings.
The loss was just the second for the Royals in nine overtime games this season.
Until Young's home run, the Mets had gone nine innings without a run. They jumped ahead of right-hander Wade Davis in the first inning. Lagares slapped a one-out single, and David Wright pounded a home run over the left-field fence for a 2-0 lead.
"Wade Davis did a great job," Yost said. "Just one pitch, and the pitch wasn't even a horrible pitch. It was kind of down-and-in to an All-Star that golfed it out of the ballpark."
That handed support to right-hander Dillon Gee, who shut down the Royals for seven innings before being relieved after issuing a walk to start the eighth.
"We do it all the time," the Royals' Johnson said. "It seems like we really put things together in the late innings. It's the early innings that give us some trouble sometimes, whether we win or lose."
Indeed, the Royals didn't get their first run until the eighth. Cain drew the walk from Gee. Reliever Scott Rice nicked Gordon with a pitch and Cain finally scored on the last of two forceout plays.
Wade Davis kept busy working his way out of jams. After pitching his only 1-2-3 inning in the fifth inning, Davis was pulled for a pinch-hitter to start the sixth. Along with two runs, he gave up eight hits with no walks and five strikeouts. He threw 104 pitches.
He got good backing from the bullpen's Kelvin Herrera, Louis Coleman and Crow, who combined for four scoreless innings. Coleman threw two perfect innings.
The Royals' hot streak -- the nine straight was part of an 11-2 surge after the All-Star break -- came at a time the American League Central teams ahead of them also were rolling. The Tigers won their sixth straight on Friday night, while the Indians had their streak ended at eight.
"We had to do it," Johnson said. "Imagine if we weren't winning. Think of how those teams are playing. And finally Cleveland mixed in a loss today, but Detroit won again, what a shocker. You always say, worry about yourself and win, but it'd be nice if they could mix in a few losses for us."
The Royals, despite all the recent victories, are 7 1/2 games behind the Tigers.
One streak was over, but the Royals were looking ahead.
"Nine out of 10, I think any team would take that," Crow said. "Just go out there tomorrow and start a new one."
"It never feels good after you lose a game, but yeah, it was a nice streak," Yost said. "Now let's see if we can start another one."