Kansas City's first home victory of the season came just hours after Rivera suffered what an MRI revealed to be a torn anterior cruciate ligament and meniscus in his right knee chasing a batting practice fly ball.
"You lose a Hall of Famer; that changes [our team] a lot," Yankees manager Joe Girardi said. "The depth of our bullpen just got a little bit shorter because of the injury. We've got to find a way to get through it."
Rodriguez said it was impossible not to think of Rivera during the game, and Mark Teixeira said that he asked a few times during the game about Rivera. Derek Jeter, who had four hits -- including his 500th career double -- said the Yankees had to go on.
"We have no choice. You can't sit around and feel sorry for yourself," Jeter said. "You feel sorry for Mo. I'm pretty sure most people feel sorry for him, but no one is going to feel sorry for the Yankees."
Phelps had to do his best to block out those distractions. Pitching in front of a group of friends and family that made the trip from his hometown of St. Louis, Phelps held the Royals to two runs and six hits.
"A couple of times I let my emotions get the best of me," Phelps said. "I was trying to do a little bit too much out there. That last inning, I finally just let my pitches work and get some ground balls rather than trying to throw everything by people."
The rookie right-hander was upset, however, that he needed 85 pitches to get through four innings and was bounced earlier than the Yankees had hoped.
"It's frustrating that I wasn't as efficient with my pitches as I would have liked to be, but I just tried to keep the team in it as long as I could," Phelps said.
Phelps, who made the club as a long reliever out of Spring Training, walked none and struck out five in the effort. He figures to receive at least one more turn in the rotation as the Yankees continue to hold the fort until Andy Pettitte's projected big league return later this month.
"I haven't heard anything yet. We were just focusing on today, trying to win a ballgame," Phelps said.
Kansas City's Mike Moustakas crushed a solo home run in the second inning off Phelps, his fourth, and Eric Hosmer knocked in Jarrod Dyson with a third-inning RBI single. Moustakas added a big two-run single facing rookie D.J. Mitchell in the fifth to open up a 4-1 lead at the time for the Royals.
The Yankees weren't able to do much with left-hander Danny Duffy, whose hard-throwing arsenal limited New York to two runs and six hits over 5 1/3 innings. Duffy walked two and struck out six.
"Man, a lefty that throws 99 [mph]," Teixeira said. "You just don't see it. That's a really good arm. He pitched very well."
Jeter scored twice after Girardi shook up the heart of his lineup for Thursday's game, seeing some signs of life from the struggling sluggers.
Teixeira drove in two of New York's runs with a well-struck third-inning double and a seventh-inning sacrifice fly, while Eduardo Nunez lifted a sixth-inning sacrifice fly to bring home another Yankees run.
The Yanks nearly tied it in the ninth as Jeter opened with his fourth hit, off closer Jonathan Broxton. Curtis Granderson drew a walk, drawing memories of the 2010 game when the Yankees toppled Broxton -- then with the Dodgers in Los Angeles.
Colin Curtis and Chad Huffman were the heroes that night, but they were nowhere to be found in Kansas City as the Royals pulled off a key double play, with second baseman Chris Getz diving to stop Teixeira's shot up the middle, flipping to shortstop Alcides Escobar, who somehow got off a one-bounce throw that first baseman Hosmer snagged for the second out.
The count went full on Rodriguez before he bounced out to Moustakas at third base, who rushed in, grabbed the ball and nicked A-Rod at first to send the Yankees to what felt like their second loss of the day.
"We had a lot of opportunities, but we just couldn't get the big hit," Girardi said. "It's unfortunate."