Sogard doubled off Matt Hall (0-1) with two outs and Tommy Pham was intentionally walked. Brosseau, batting for pitcher Colin Poche, singled to right-center field for the Rays' first run since Wednesday, ending a streak of 29 scoreless innings.
"Obviously a long game, right? So you want to be the one to end it in that situation," Broussard said after his first walk-off hit. Six Tampa Bay pitchers combined to set a major league record for strikeouts without a walk, and it also set a franchise record for the Tigers, who have struck out 37 times in the first two games of the three-game series without a base on balls.
"I know we struck out as many times as I've ever seen in a baseball game," said Detroit manager Ron Gardenhire. "A lot of outs were being made and that's probably because the pitching was pretty good on both sides."
Sogard's double off the wall was the only hit that came close to a home run on a night when plenty of hitters were trying to hit one. "I think in those situations everybody wants to hit the game winner," Gardenhire said. "When you start swinging hard and out of the (strike) zone trying to do those things, it really works against you. Both teams kind of got involved in that a little bit."
Rays relievers struck out 14 in 20 hitless at bats. Six Tigers hitters struck out at least three times. "(Rays starter Ryan) Yarbrough set the tone from pitch one," said reliever Emilio Pagan, who struck out four in two innings. "We were in a lot of plus counts and we were able to execute when we were ahead. That was a special game for sure."
Poche (3-4) got the win after striking out two of the three Tigers he faced in the 13th. The win kept the Rays one-half game ahead of Oakland for the American League's second wild-card spot. Detroit's final hit was Niko Goodrum's one-out double in the seventh off Yarbrough. The next eight Tigers struck out against three different relievers.
Yarbrough, who came one out short of pitching the Rays' first complete game in three years on Sunday, is 6-0 with a 1.43 ERA over 56 2/3 innings in his last 11 appearances. He gave up three hits while striking out 10 in 6 1/3 innings.
Detroit starter Jordan Zimmermann allowed only one baserunner — on Tommy Pham's double — in five innings, throwing 63 pitches and striking out five. ANDERSON'S K's Since allowing a double to Boston's Andrew Benintendi, the first batter he faced as a Ray, Nick Anderson has retired 21 straight, 17 by strikeout. He struck out the side in the eighth inning Saturday. Anderson was acquired in a trade from Miami on July 31.
TRAINER'S ROOM Tigers: C Grayson Greiner (lower back strain) moved from Class A Lakeland to Triple-A Toledo for the final step of his rehab process. Rays: 2B Brandon Lowe, out since July 3 with a bruised right shin bone, will play with Class A Charlotte through Sunday at which time it will be determined if he will join Triple-A Durham. "It will be depended on if everybody feels he's moving well," manager Kevin Cash said. "If not we'll just keep him at Charlotte."
UP NEXT Tigers: LHP Matthew Boyd (6-9) will pitch Sunday's series finale. He has given up 11 earned runs over eight innings in his last two starts. Rays: RHP Trevor Richards was added to the taxi squad from Triple-A Durham and will start Sunday. Acquired from Miami on July 31, Richards went 3-12 in 23 games for the Marlins. The Rays optioned RHP Pete Fairbanks to open a roster spot for Richards.
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