The win salvaged a series split after the Orioles dropped games on Monday and Tuesday, and improved Baltimore's record to 18-6 in one-run games.
"We're resilient," Reynolds said. "We've had a tough run here lately. To get these last two games, especially to come back from behind today with a win, will hopefully give us a little momentum moving forward and keep playing better baseball."
Matt Wieters and Wilson Betemit took back-to-back one-out walks from Minnesota reliever Alex Burnett in the eighth, prompting the Twins to call on left-hander Tyler Robertson against Chris Davis. Davis grounded out, but Reynolds then came through to score Wieters and Betemit against reliever Anthony Swarzak.
"We walked ourselves into a mess there in the end," Twins manager Ron Gardenhire said. "Walks get you every time in situations where anything can happen. And a bloop to center field ended up costing us a couple runs. So that's how you lose a ballgame at the end -- with walks."
Baltimore had been 0-for-7 with runners in scoring position and entered the game 9-for-56 (.161) in scoring situations over the previous eight games.
"The thing that you have to keep in mind as a player -- nobody in the locker room knows that stat," manager Buck Showalter said. "Sometimes ignorance is bliss. But they know. It's not like they're not trying. Sometimes you can want something too much and grip the sawdust out of the bat."
The bullpen also came through admirably, holding onto a one-run lead for the second straight game. Neither Darren O'Day or Troy Patton could record an out in the eighth, as O'Day walked Josh Willingham and Patton allowed a single to Justin Morneau.
Showalter then turned to Pedro Strop. The right-hander retired all three batters he faced.
"It was a tough situation right there, like every eighth inning," Strop said. "My mindset was focused on the first out, because I know I can get a hard ground ball. I was like, 'If I get the first out, I'm going to for sure try to get a ground-ball double play and I'm going to get out of it as quick as possible.'"
Before Reynolds' timely hit, the Twins clung to a 3-1 lead after Alexi Casilla's sacrifice fly off starter Wei-Yin Chen in the fourth. Baltimore scored a run in the seventh to trim the lead to 3-2, but stranded the potential tying run.
Davis led off the seventh by drawing a walk from Brian Duensing, which was followed by a single from Reynolds. Ryan Flaherty's sacrifice bunt moved the runners to second and third.
Nick Markakis then rolled a slow grounder toward third. Trevor Plouffe scooped the ball and tried to gun down Davis at home, but his throw was too high for catcher Joe Mauer to handle, and Davis crossed home for Baltimore's second run.
Minnesota intentionally walked J.J. Hardy and pitted the left-handed Duensing against former Twins slugger Jim Thome. That decision paid off as Thome grounded into an inning-ending double play.
Baltimore's first run came on a solo homer from Davis in the second inning, his 15th of the season.
Chen's day started in shaky fashion with a two-run first inning. Ben Revere's one-out infield single was followed by a walk to Mauer and an RBI single by Willingham. Chen struck Morneau out, but Plouffe hit a double to score Mauer and give the Twins an early 2-0 lead.
The left-hander allowed only three additional hits after the first inning.
"The first inning, I tried to pitch too cautious, and that's why I struggled a little bit," Chen said through a translator. "But after the first inning, I just changed my eye level on them, and everything [was] fine. I just kept pitching and just throwing hard."
The win snapped a losing streak for Chen, giving him his first win since June 17 at Atlanta. Baltimore has given Chen just 30 runs of support over his last 12 starts.
"You can only do what you can do," Showalter said. "Starting pitcher, probably the least thing he controls is the [win]. You can't control the defense, you can't control the runs scored. But if you're consistent getting deep into games, you're going to win your share."