Young ripped Farnsworth's 1-0 pitch 427 feet into the seats in left-center for his first career game-winning homer. Young leaped into the air as he approached home plate, diving into a group of teammates there to greet him.
"It felt good," Young said. "Hitting a home run was the last thing on my mind, facing a guy who's got really good stuff. I was just thinking contact, get on base, and set the table for the guys behind me. It was cool ... when it helps the team out, it's always a good feeling."
The Rangers were searching for something positive after losing seven of their previous eight and dropping the first two games of the series to the Royals by a combined score of 14-3.
"We needed it," Young said. "Fortunately we got some breaks there in the eighth and tied it up. Hopefully we can get some momentum out of this win and take it on the road."
The Rangers trailed 5-3 when Andruw Jones doubled off reliever Ron Mahay in the eighth. Jones went to third when Royals first baseman Mike Jacobs booted Hank Blalock's grounder, and he scored on Nelson Cruz's ground out off Jamey Wright to make it 5-4.
Blalock went to second and Chris Davis followed with a pinch-hit single, with Blalock scoring when Davis' sharp grounder glanced off the glove of second baseman Alberto Callaspo. Callaspo recovered the ball and threw home, but Blalock's slide avoided the tag from catcher John Buck.
Frank Francisco (1-0) pitched a perfect ninth for the win.
Ian Kinsler, who homered and went 2-for-4, was standing next to Davis on the top step of the Rangers' dugout when Farnsworth threw the second pitch to Young. Davis and Kinsler grabbed each other as the ball sailed into the seats, then sprinted onto the field to await Young's arrival.
"The most fun is waiting for him to get to the plate because after that it's just chaos," Davis said.
Farnsworth said missing the strike zone with his first pitch proved disastrous.
"You don't like getting behind in the count," Farnsworth said. "You have to throw a fastball and that's what he wants."
Farnsworth has struggled early as the losing pitcher in three of the Royals' five losses.
"He hasn't gotten off to a good start," Kansas City manager Trey Hillman said. "He's made improvements to his delivery. But he's had more tough outings than positives. We've seen some good things out of him, but to do what we want to do, Kyle Farnsworth has got to perform for us."
Royals starter Kyle Davies recovered from a four-walk first inning to pitch three-hit ball over six innings, leaving with a 5-3 lead before the bullpen faltered.
Davies fell behind 2-0 in a shaky first but righted himself to allow three runs, strike out eight and walk five.
Jacobs and David DeJesus homered and drove in two runs each for the Royals, who had won five of six entering Sunday's game.
Texas starter Vicente Padilla allowed five runs and eight hits in five innings with five strikeouts and one walk.
Davies had trouble finding the strike zone in the first, walking four with Kinsler and Young executing a double steal. Blalock's sacrifice fly and David Murphy's bases-loaded walk gave Texas a 2-0 lead.
"I tried pounding the fastball but I just couldn't locate it," Davies said. "I should have gone to the breaking ball. I needed to make the adjustment a little sooner. It went a little too far in the first inning."
Jacobs' two-run homer in the second tied it at 2-2.
Kinsler's homer in the second put Texas ahead 3-2, but DeJesus' RBI single in the third tied it at 3.
Buck's RBI single in the fourth gave the Royals a 4-3 lead, and DeJesus' solo homer in the fifth made it 5-3.
Meanwhile, Davies settled in after Kinsler's homer, retiring 14 of the next 16 batters.
Hillman said right-hander Zack Greinke is on track to join the game's elite pitchers. Greinke tossed his first major league shutout in beating the Rangers on Saturday night, extending his shutout streak to 34 innings dating to last season. "He's on a roll," Hillman said. "That was about as good as it gets. I think Zack can be one of the premier pitchers in the major leagues.". ... Davies threw 37 pitches (22 balls) in the first inning. ...Texas C Taylor Teagarden made his third start of the season, striking out three times. Regular C Jarrod Saltalamacchia has been struggling at the plate, batting .176 after 11 games, but manager Ron Washington said Saltalamacchia has improved at calling a game and blocking balls in the dirt. ... Texas slugger Josh Hamilton struck out seven times in the three-game series.