The Reds can forget about that defensive debacle in between, three errors in the third inning that led to three unearned runs for Texas and likely took a victory away from starter Mike Leake.
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"We made a bunch of mistakes, but they kept fighting and fighting, and that's all that matters that we got a win," manager Dusty Baker said. "I looked up there and they had one hit and three runs -- that's rare to see that. Usually Joey (Votto) doesn't make errors, Zack (Cozart) doesn't make errors. It's one of those nights."
The Reds and Rangers both played their 81st game, reaching the midpoint of the regular season. Texas (47-34) has a half-game lead over Oakland while Cincinnati (46-35) is is in third place in the NL Central, a season-high 4½ games behind division-leading Pittsburgh.
J.J. Hoover (1-5) got the last two outs in the 10th, even after a walk and a hit. Aroldis Chapman worked the 11th for his 20th save in 23 chances.
With runners at first and third for Texas in the 10th, Adrian Beltre had an inning-ending foul pop caught by catcher Mesoraco.
A.J. Pierzynski drew a leadoff walk in the 11th, but Mitch Moreland -- whose deep flyball leading off the bottom of the ninth was caught by right fielder Jay Bruce against the wall -- then grounded into a double play.
Cincinnati had lost six of seven games overall and was coming off consecutive shutout losses before Choo's fifth leadoff homer this season, and 12th overall. The Reds had also lost five consecutive interleague games.
"Every streak starts with one. You got to get one before you get 10, six or whatever it is," Baker said. "I think one game can get you going. And the way you win it gets you going sometimes too."
Mesoraco was 0 for 4 with three strikeouts before his 380-foot homer into the left-field seats off Kyle McClellan (0-1), which came right after Todd Frazier was hit by a pitch to start the 11th.
"Baseball's a crazy game. I think sometimes when you're struggling you try harder, but in reality you try less just because if you're going up there and you're grinding and you're trying to get a hit, most of the time you're not going to do it," Mesoraco said. "I think it's just a matter of going up there, relaxing and staying within yourself."
Leake allowed only three hits and one earned run in seven innings. But Cincinnati had three errors in the third when Texas scored three unearned runs.
"He's thrown the ball as well as anybody in the league and he really deserved better than what he got," Mesoraco said.
The Rangers had only one hit before consecutive doubles by Elvis Andrus and Nelson Cruz to start the sixth for a 4-all tie.
"We had one hit for a long time and three runs, so they kind of gave us three runs," Pierzynski said. "Their pitcher did a great job keeping us off balance and we had a couple of chances we didn't cash in. We did cash in a couple that we shouldn't have, so it evens out."
Two of Cincinnati's three errors came on fielder's choice plays that produced runs as Texas went ahead 3-2 in the third.
All-Star first baseman Votto made two errors, the first when he was unable to pick up the ball after a grounder hit off the heel of his glove. Leonys Martin, the No. 9 hitter, followed with a single to extend his hitting streak to 13 games before consecutive fielder's choice plays.
Votto made a nifty backhanded stop of Ian Kinsler's grounder, but he threw wide of home unsuccessful trying to get a runner. The throwing error allowed other runners to advance to second and third before Andrus hit a RBI grounder to shortstop Cozart.
With Kinsler also running, Cozart's wide throw forced third baseman Jack Hannahan to reach away from the bag for the third Cincinnati error in four batters. Kinsler stopped momentarily before jumping onto the bag and avoiding the tag. Cruz then had a sacrifice fly.
After going 1 for 19 his previous six games, Choo hit the first pitch into the visitors bullpen in left-center field. That snapped a stretch of 20 consecutive scoreless innings by Texas pitchers that included a 4-0 victory in the series opener Friday night.
Choo walked twice and had three hits, including a leadoff single in the ninth before he was caught stealing to end that inning.
Texas rookie right-hander Nick Tepesch struck out seven, but was gone after allowing three consecutive hits to start the fifth.
The Reds got an unearned run in the top of the third when Derrick Robinson reached on an error by second baseman Jurickson Profar and scored on a bloop single by Brandon Phillips. ... Votto has 10 errors in 80 games this season. He had six in 109 games last year. ... Tepesch is winless in eight starts since his last win May 12 at Houston. He won his major league debut April 9 against Tampa Bay, but is winless in seven starts at Rangers Ballpark since.
44,397 (92.1% full) - % is based on regular season capacity
97 degrees, clear
Home Plate - Mike DiMuro, First Base - Ted Barrett, Second Base - Will Little, Third Base - Scott Barry
Since June 11, Leonys Martin has hit .458 in at-bats ending in a fastball or sinker, fourth highest in the AL during that span. Mike Leake has allowed a well-hit ball in 24 percent of at-bats ending in his fastball or sinker, fourth worst among 45 NL pitchers with at least 15 starts.