CHICAGO -- For a moment on Wednesday, it looked as if the Rays might suffer yet another defeat in the same style they’ve seen throughout their series at Wrigley Field. Tampa Bay’s starter gave the team everything it could’ve asked for on the mound, but the bats had yet to awaken from their three-day slumber.

Come the seventh inning, though, the Rays finally got the big hit they’d been waiting for. One inning later, they got another one for good measure.

Brandon Lowe slugged Tampa Bay’s first homer of the series, tying the game in the seventh with a two-run blast. Though Chicago quickly regained the lead, Jose Siri’s go-ahead two-run shot in the eighth gave the Rays the lead for good, helping them secure a 4-3 win and avoid being swept for the first time this season. It also made them the first team in the Majors to reach 40 wins.

“We're the type of team that doesn’t like to give up,” Siri said through interpreter Manny Navarro. “We can do a lot of different things. We have the power. We have the pitching.

“Everyone's going to have their two-, three-, four-game stretch where they're going to do bad in the season. Sometimes, some teams have a week-long [stretch]. But we're the type of team that, you know, we don't let a bad streak affect us.”

The victory served as a silver lining to what had been a trying set in Chicago. The Rays’ bats were quieted through the first two games, and they weren’t faring much better six frames into Wednesday’s contest. Cubs starter Justin Steele and reliever Hayden Wesneski held Tampa Bay to one hit all the way into the seventh.

The tide finally turned when, after a Manuel Margot walk ended Wesneski’s day, Lowe greeted Cubs reliever Mark Leiter Jr. with a Statcast-projected 431-foot blast to dead center. It was the Rays’ first extra-base hit of the series, and the impact it had on the club was hardly understated.

“Brandon’s [home run] changed the whole mindset of the dugout, for sure,” manager Kevin Cash said. “For whatever reason, I can't put my finger on exactly why, but the bats kind of went quiet a little bit. It's going to happen over the course of the season. But you like to -- when you're within striking distance in a one-run, two-run ballgame -- to be able to get somebody on base and then knock one out. We did it twice today.”

Though Lowe’s blast tied the game at 2 and brought new life to a temporarily slumping offense, the Rays found themselves behind again a half-inning later. Starter Zach Eflin allowed a leadoff double to right fielder Seiya Suzuki, who went on to score after Trey Mancini laced a liner into left off reliever Colin Poche for an RBI single. Eflin finished the day allowing three earned runs and striking out five over six-plus innings, going at least six frames in his sixth straight start.

It initially appeared as though Tampa Bay’s long-awaited clutch hit was going to come in a losing effort. But that’s when Siri came through in the eighth, pounding his chest as he rounded the bases on what turned out to be a game-winning two-run shot.

“Their slug finally showed up, and that's what beat us today,” Cubs manager David Ross said.

With another pair of homers, the Rays have ensured a little history at month’s end, becoming the first team to lead the Majors outright in both homers (103) and stolen bases (77) at the end of May since the 1955 Brooklyn Dodgers (per the Elias Sports Bureau).

But Tampa Bay wouldn’t have been able to seal the win without another strong -- yet dicey, at times -- effort from a scuffling bullpen.

Jason Adam dodged trouble in the eighth, striking out two straight batters after putting runners at first and third with one out. And after Kevin Kelly loaded the bases with one out in the bottom of the ninth, Jalen Beeks retired the final two batters -- running the count full on both -- to secure the save.

Asked if he was expecting to close out the game, Beeks said, “No, but it is the Rays, so you always got to be ready.”

It was the kind of win the Rays badly needed to erase what had been a frustrating funk at the plate. And the kind they've come to expect from themselves this season.

“It was a great team win,” Eflin said. “The feel in this clubhouse is just, everybody has each other’s backs. That was kind of Exhibit A today.”