Eyre came into the game in the 10th inning, and he threw two scoreless innings until the 12th.
Ryan Braun reached safely to begin the inning, after Ian Kinsler fumbled a ground ball. Eyre was then hit in his left calf by a Corey Hart line drive. Hart was able to reach safely as the ball rolled away from Eyre. With Braun and Hart on first and second, Jenkins unleashed his 11th home run of the season.
"My calf didn't have any effect on it," Eyre said. "I was fine, felt good and made a lot of good pitches -- just not that one."
It looked like the Rangers might make their second comeback of the game in the bottom half of the inning. Marlon Byrd led off with a single to left, his fourth hit of the night. But Michael Young flied out to right, and Sammy Sosa grounded into a game-ending 4-6-3 double play.
The hopes of a second consecutive comeback victory and their second sweep of the season ended.
"We played well," Young said. "We fought back in the ninth against a great closer. It didn't help us in the standings, but we fought hard, and hopefully we can take something from this."
Despite the loss, Byrd continued to be impressive at the plate, especially in pressure situations. He got the game-tying hit with a broken-bat RBI single in the ninth off Brewers closer Francisco Cordero. It was the second consecutive night Byrd, who has a nine-game hitting streak, got a hit off one of the best closers in the game. More impressively, both times, he was facing a 0-2 count.
"I don't know," Byrd said. "Last night, he came with sliders and tonight he tried to come in."
"My bat broke, but it died a champion. That's baseball. Sometimes it works out that way. I'm seeing the ball well right now."
Byrd, who hit in the No. 2 spot, scored in the first after a successful bunt. He scored again in the third, on an RBI single by Young. In the seventh, Byrd had an RBI single to cut the Brewers' lead to one.
"Byrd can find some holes," Milwaukee manager Ned Yost said. "He didn't hit it hard all the time, but he killed us tonight."
Still, the Rangers fell short.
"[I thought] things were going to go our way the whole game, but that's just baseball," Rangers manager Ron Washington said. "It was a good game, and they just ended up pulling it out."
Texas starter Vicente Padilla threw 4 2/3 innings, allowing 11 hits with five strikeouts. Despite the high hit total, he held Milwaukee to two runs. He gave up a two-run home run to Prince Fielder in the fifth inning and left the game with the Rangers leading, 3-2.
"He kept runs from crossing the plate," catcher Gerald Laird said. "When he needed to make a pitch, he did."
It was Padilla's first start since missing his last one with irritation in his right triceps.
"He did a good job changing speeds and keeping them off balance," Washington said. "He was just one pitch away from getting out of the fifth."
The Rangers jumped out to a 2-0 lead in the first, with Kenny Lofton and Byrd scoring. They kept a one-run lead into the sixth.
With two outs in the sixth, the Brewers rallied for three runs to take a 5-4 lead. Reliever C.J. Wilson, who came in for Wes Littleton, hit two batters and gave up two runs. The other run was charged to Littleton.
Brewers second baseman Craig Counsell gave his team a 6-4 cushion with a solo home run off Frank Francisco in the seventh.
Milwaukee got 22 hits on the night, but the Rangers kept it close with good pitching and timely defense.
In the 11th, Lofton kept the Rangers in the game. Tony Gwynn Jr. was on second when Tony Graffanino singled to center. Lofton fielded the ball and gunned down Gwynn at the plate for the second out. Recently acquired catcher Adam Melhuse tagged Gwynn out, and Eyre escaped with no damage. Eyre had tossed 14 1/3 scoreless innings before Jenkins' home run.
"He's only human," Washington said. "It was just like Cordero last night. He'll regroup and get back on track."
The Rangers used seven pitchers on the night. It was the longest game, 4 hours and 20 minutes, of the season for the Rangers, too.
Texas won the series and will try to carry that momentum into its upcoming six-game road trip, which begins Tuesday in Pittsburgh.
"There's a lot more life in here the past two days," Eyre said. "We're excited to go on the road."