The Rangers, who were 4-11 at one point in June, won 10 of their final 13 games to finish 15-15 for the month. That included taking two of three from the Reds, as Texas remains a half-game ahead of the Athletics in the American League West.
"It's the best .500 month ever -- to go from where we were and the stretch we knew we had in front of us, the teams we were playing on the road that are tough places to play and to be able to go in and win," said closer Joe Nathan. "To be able to grind through and believe we can play better than we have, obviously, and win series against playoff-caliber teams down to the end speaks volume for this clubhouse. Guys knew not to give up and keep pressing on."
Leonys Martin, still hitting at the bottom of the order, sparked the Rangers' offense with two hits and two runs scored. He has now hit in 14 straight games, with 20 hits in his last 49 at-bats.
Darvish, who earned his first victory since May 16, allowed four hits and four walks while striking out eight. He threw 117 pitches and is now 8-3 with a 2.78 ERA and a league-leading 151 strikeouts on the season.
"As a starter, if the team doesn't win on the day you pitch, it can be really frustrating," Darvish said. "That was my thing."
Darvish did win over Reds starter Mat Latos in a tight pitching duel that was scoreless until the Rangers broke through with two in the bottom of the fifth. Darvish made the lead stand up, and so did relievers Neal Cotts and Jason Frasor, who bailed Scheppers out during a tension-filled eighth inning when the Rangers' 3-0 advantage appeared to be on the verge of getting wiped out.
Darvish won because of a much better fastball, which he threw 72 percent of the time over his 117 pitches.
"We wanted to be aggressive with his fastball, and that made his off-speed pitches better," catcher Geovany Soto said. "His fastball was really great today. He used the fastball and moved it around a lot better."
Darvish just needed a couple of runs, and he got them in the fifth. Engel Beltre led off the rally with a bunt single and went to third on a double by Martin. After Ian Kinsler struck out, Elvis Andrus dropped a squeeze bunt. Latos fielded it barehanded on the run and threw home trying to get Beltre. But the throw hit Beltre in the side of his face and rolled away from catcher Devin Mesoraco, allowing Martin to come around, as well.
"It was just a reaction," Latos said. "It was bunted pretty hard and I thought I could make a play on it. I just kind of made a bad throw. I put Mesoraco in a pretty crappy situation to get hit like that. Looking back at it, I should have just held on to the ball."
Beltre was momentarily stunned from getting hit but stayed in the game.
"It hit his ear, not his head," manager Ron Washington said. "I told him it was still there. There weren't any lacerations and there wasn't any blood."
The Rangers added another run in the seventh, as Martin led off with a single, stole second and scored on a one-out single by Nelson Cruz.
The Rangers needed the run. Scheppers took over in the eighth and quickly loaded the bases on a walk to Zack Cozart and singles by Joey Votto and Brandon Phillips. When Scheppers fell behind, 2-0, to Jay Bruce, Washington rushed Cotts into the game.
"It was just one of those days," Scheppers said.
Cotts gave up sacrifice flies to Bruce and Chris Heisey. Frasor then took over and retired Todd Frazier on a fly to center to end the inning. Nathan, who has been successful on 11 straight save opportunities, then retired the side in order to end the game and the Rangers' taxing month of June.
"We're playing good baseball, that's what we want to do," Washington said. "We have a lot of ball left, so we have to keep grinding. The last few games against Cincinnati were tough, so we have to keep grinding. We've got to play the game just like that. If we do, the other stuff will fall into place."