ST. PETERSBURG -- The Rays' pitching staff has been one of the best in the Majors this season, but its performance on Saturday was one of the best in franchise history, and Tampa Bay needed every bit of it.

Michael Brosseau delivered the big walk-off hit in the 13th inning to give the Rays a 1-0 win over the Tigers at Tropicana Field, snapping a 29-inning scoreless streak for Tampa Bay's offense.

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But it was the pitching staff that set the tone and helped the Rays secure their 72nd win of the season.

Led by Ryan Yarbrough’s career-best 10 strikeouts, the Rays used six pitchers to set a single-game club record with 24, surpassing their 22 in an 18-inning game on June 27 against Minnesota.

According to the Elias Sports Bureau, Major League Baseball's official statistician, the Rays also set a Major League record by recording 24 strikeouts without allowing a walk in a single game, surpassing the Red Sox’s 22 on May 8 this season against the Orioles. Tampa Bay also set a club record with 37 strikeouts over consecutive games, surpassing the 32 they had accomplished four times, most recently on Aug. 9-10, 2014.

In the two games of this series against the Tigers, the Rays have recorded 37 strikeouts without allowing a walk in 22 innings.

“The pitching has been outstanding,” Rays manager Kevin Cash said. “Charlie [Morton] was outstanding yesterday, and today Yarbrough followed suit, and everybody that came in from the bullpen was dominant. That was a really dominant performance. … We have a special group down in that bullpen.”

“I guess we could say both teams pitched really well for it to go that deep and that long with nobody scoring, but I know we struck out as many times as I’ve ever seen in a baseball game,” added Tigers manager Ron Gardenhire. “We had to really finagle our way through some situations. … It kept going on, and finally, you know, [the Rays] got us.”

While Yarbrough set the tone, the Rays’ bullpen picked up right where he left off. Chaz Roe struck out the two batters he faced to keep the game tied in the seventh inning, and Nick Anderson, who was acquired from the Marlins on July 31, struck out the side in the eighth inning, extending his streak to 21 batters retired. Anderson is also the first reliever to start his Rays career with seven straight appearances with multiple strikeouts.

Emilio Pagán, Diego Castillo and Colin Poche also did their part, striking out nine over five scoreless innings.

As a whole, the Rays' bullpen struck out 14 of the 20 batters it faced and helped secure Tampa Bay's eighth shutout of the season.

“As a pitching staff as a whole, it’s incredible,” Yarbrough said. “It was incredible on the pitching aspect, just seeing how efficient and how they were blowing guys away with their stuff. It’s incredible, and obviously you’re really happy for a bunch of those guys with how they’re throwing.”

The pitching performance helped set the stage for Brosseau, who was the last available position player on the Rays' bench.

After Eric Sogard hit a two-out double to start the rally, the Tigers elected to intentionally walk Tommy Pham to force the Rays to pinch-hit for the pitcher. Cash went to Brosseau, and the rookie delivered with the walk-off hit to the right-field gap. It was the fourth walk-off win of the season for the Rays.

“It felt amazing,” Brosseau said. “To be put in that situation and come through for this team, who played an unbelievable game. I know the offense wasn’t where we wanted to be all game, but our pitching staff held it down all game and gave us a chance all game, and I’m happy to pull through for them.”

The Rays avoided back-to-back loss to the Tigers, who hold the worst record in the Majors. With the A’s winning on Saturday, Tampa Bay needed a victory to hold on to the second spot in the American League Wild Card race.

“That was a big win,” Pagan said. “Detroit played us tight the last two days, [but] to set ourselves up to win a series is big. We win a lot of series, we give ourselves a chance to get in the postseason, so I’m just happy to get the W.”