DETROIT -- Nick Castellanos needed that.

His well-fought three-run triple with two out in the eighth inning Wednesday night gave the Detroit Tigers a 5-2 victory over the Milwaukee Brewers.

Detroit avoided getting swept in a series for the first time this season.

"I've been waiting for that all season," Castellanos said after winning his battle with right-handed reliever Jonathan Broxton (1-1). "I needed it, the team needed it, the fans needed it, we all needed it."

Broxton fed Castellanos a steady run of fastballs until the Detroit third baseman laced a shot to the wall in right field that shot by right fielder Gerardo Parra and cleared the bases.

Tigers right fielder J.D. Martinez had singled with two outs and gone to third when Detroit left fielder Yoenis Cespedes poked an outside pitch to right for a single. Broxton walked left-handed-hitting designated hitter Tyler Collins to load the bases and face the right-handed Castellanos.

"That was a good at-bat," manager Craig Counsell of Milwaukee said of the Castellano-Broxton battle. "He was throwing 96, 97 (mph) and Castellanos kept fouling them off. The pitch he hit was 96, 97.

"Broxton had good stuff. Castellanos just put a good at-bat on him."

"The more fastballs I saw," Castellanos said, "the more comfortable I got."

"Broxton gets out (second baseman Ian) Kinsler and (first baseman Miguel) Cabrera but they've still got good hitters coming up," Counsell said. "Cespedes, that was a good at-bat. Collins was pitched well to but he showed some patience and walked.

"I felt like his stuff was where it should be, but I felt they earned the win on their at-bats."

The win went to left-hander Blaine Hardy (2-0), who got one out in the eighth. Right-hander Joakim Soria pitched the ninth for his 13th save.

Right-hander Shane Greene, limited to five innings and 74 pitches in his previous start because of tingling and numbness in two fingers, threw 106 pitches and made it through 6 1/3 innings before manager Brad Ausmus brought in right-hander Angel Nesbitt after a one-out walk to left fielder Khris Davis.

Shortstop Luis Sardinas squeezed a single down the left-field line past an over-shifted defense, moving Davis to second base, and second baseman Elian Herrera tied the score at 2 with a bloop double just inside the right-field line.

With the infield in and Sardinas going on contact, catcher Martin Maldonado lined into a double play to short to end the inning.

Greene gave up two runs, three hits and two walks while striking out six.

Right-hander Kyle Lohse went the first six innings for Milwaukee, allowing two runs, seven hits and two walks with four strikeouts.

The Tigers loaded the bases with three straight singles to start the fourth but could only get one run out of it. Castellanos got the RBI to put Detroit ahead 2-1 when he beat out the relay of a force play at second. Rookie catcher James McCann then hit into a double play.

"You bust it down the line there because you want the RBI," Castellanos said. "I was just trying to get the run in any way I could. Hit, sacrifice fly, hit by pitch, walk, anything. The forceout was okay because with runners on first and third and one out you've got a chance for another RBI."

Designated hitter Ryan Braun hit the first pitch of the top of the fourth for his 10th home run of the season to create a 1-1 tie for Milwaukee.

Detroit scratched out a second-inning run. Cespedes doubled to left center, stole third and scored when Maldonado's throw went into left field for an error.

NOTES: Milwaukee 3B Aramis Ramirez hit his fifth home run of the season Tuesday night. It was his 369th as a third baseman, which put him ahead of Graig Nettles for fifth-most home runs by a third baseman. ... Detroit RHP Bruce Rondon (right biceps) will pitch Thursday and Sunday as the beginning of a rehab assignment at Triple-A Toledo. ... Ryan Braun was Brewers manager Craig Counsell's choice to DH for a second straight game "because I thought it was good time to do it. Ryan's been in there (the outfield) every day." ... The Tigers scored two or fewer runs 19 times this season entering Thursday, and they owned a 6-13 record in those games.