"It's what I've got to do," Reynolds said. "It's the situation I'm in. When I'm there, I'll be ready to go."
The win moves the O's into the American League's second Wild Card spot, finishing a stretch of 30 games in 31 days ahead of Monday's off-day.
"We're definitely tired," shortstop J.J. Hardy said. "We're all going to enjoy our off-day, but today was a huge win for us."
With the game tied at 3 in the sixth, Adam Jones and Lew Ford drew consecutive one-out walks before Royals starter Bruce Chen was lifted for Louis Coleman. Coleman threw Reynolds a 2-2 slider right down the heart of the plate, allowing the O's first baseman to reach down and smack it into left field.
Reynolds was hitting just .210 with only nine home runs and 34 RBIs entering Sunday, prompting questions about his role with the O's in the wake of Machado's arrival.
"Mark made a big contribution," manager Buck Showalter said. "I still think at some point he's going to make somebody pay. He's done some good things for us offensively, just not as consistently as he would like to."
Reynolds also made an impact in the field, snaring a sharp grounder off the bat of Chris Getz to strand runners at second and third in the fourth.
Reynolds even added a pair of challenging catches to retire batters at first, completing a double play with a sweeping scoop in the second and ending the eighth with a barehanded snag of Pedro Strop's desperation flip.
"[Reynolds] doesn't want to let his team down," Showalter said. "He's made a lot of contributions this year, especially going over to fire base and kind of settling that down defensively for us. We all know what he's capable of offensively. If I know Mark, he'll continue to be ready when called on."
Machado started at third base for the fourth day in a row, and the O's top prospect continued to impress.
Machado gave the Orioles a 2-0 lead in the second inning when he drove a sinker from Chen out to right-center field.
The hit was originally ruled a double before being overturned by video review, allowing Machado to trot home from second with his third home run of the series.
"I was impressed," Royals manager Ned Yost said of Machado. "The scouting reports we got on him said he had a couple of holes in his swing, but we couldn't find 'em. He hurt us. He actually won two games against us with homers. He's going to be a good player."
Nick Markakis snapped an 0-for-11 skid entering the series finale with a solo homer in the fifth.
The Orioles' bullpen kept the Royals quiet from there, picking up the slack as starter Tommy Hunter struggled with deep counts and lasted only five innings -- his shortest outing since May 28.
Hunter allowed three runs on eight hits, including a solo home run to Mike Moustakas to lead off the fourth.
"I kept them in there," Hunter said, "and the bullpen pretty much shut them down."
The O's 'pen threw four scoreless and hitless innings as Luis Ayala, Troy Patton, Strop and Jim Johnson chipped in a frame.
Ayala recorded the win, while Johnson nailed down his 34th save -- good for second in the league behind Tampa Bay's Fernando Rodney.
"Those guys have been doing it all year," Hunter said. "It's pretty fun to give them the ball and say, 'Here's the game, you guys go win it.' They've been doing it all year, and they're going to continue to do it."