BOSTON – Kyle Gibson's next start for the Twins will be at 7 p.m. Tuesday, roughly four hours after baseball's nonwaiver trade deadline passes. Well, unless Thursday night's brilliant 2-1 victory over the best team in baseball was Gibson's farewell.

"I'm hoping not, you know," Gibson said after limiting the Red Sox's potent lineup to four hits and one run over eight suffocating innings. "These guys are a great group of guys — and shoot, I think we can come back and make a push to the division [title], and I'm going to be excited to be a part of it."

Maybe. But on a day when J.A. Happ became a Yankee and Cole Hamels headed to the Cubs, it wasn't hard to picture some of the many scouts crowding Fenway Park sending urgent messages to their front offices: Go get this guy.

"The way he's throwing, he's an attractive piece," Twins manager Paul Molitor admitted, perhaps reluctantly, after watching the lanky righthander retire 20 of the final 22 hitters he faced in delivering his team's fourth consecutive victory. "The job he's done here — we'll have to see where that goes. He's throwing extremely well."

Gibson has been doing it nearly all season, easily the best of his five-year career, too, but Thursday's game might be his masterpiece. He struck out six, four of them coming on the third time through the order, and didn't give up a hit after the fourth inning. He reduced his ERA to 3.42 on the season, to 1.57 for his career in Boston, and he showed off his durability by throwing a career-high 120 pitches. His only run scored on a double play, and he even conquered one of his personal demons by holding AL MVP candidate Mookie Betts — 6-for-12 with three home runs against Gibson before this game — hitless in four at-bats.

In all, the righthander filmed a pretty convincing promotional tape for teams looking for stout pitching down the stretch — and for next season, too, since he is not yet eligible for free agency.

"It's been weird. But it's part of baseball, you know?" Gibson said with a shrug of the increasingly persistent rumors around him. "It's tough. You try to focus on the plan each day, not really knowing if today is the day you come in and you're going somewhere else."

The only move Gibson wants to make, after watching Mitch Garver deliver an eighth-inning double to drive in the go-ahead run, is up the standings; Thursday's victory cut Cleveland's AL Central lead to seven games, the closest the Twins have been since June 22.

"I don't think anybody in here wants to be sellers, and I know the front office wants that type of attitude out of us. We believe that we can come back," Gibson said. "And we're really confident. We're playing our best baseball. I think we're hitting our stride right at the right time, and we get to play [the Indians] at the start of next week. So [if we] keep it going into the weekend, and maybe take the first two against them, you never know what happens around the deadline."

He's right. Heck, maybe some contender will make a serious offer for Fernando Rodney, though it's hard to tell whether the 41-year-old closer's résumé was strengthened or weakened by an anything-but-routine save Thursday. Sure, he unleashed a 97-mile-per-hour fastball that Jackie Bradley Jr. couldn't touch to seal his 22nd save — but what came before it had the announced crowd of 37,439 roaring with every pitch.

Rodney surrendered a leadoff single to Xander Bogaerts, got a couple of quick outs — and then walked Blake Swihart and Brock Holt to load the bases. He then threw three straight balls to Bradley, Boston's No. 9 hitter, removing every shred of breathing room.

"[His teammates] say everybody was nervous and every piece of gum they had in their mouths, they took it out," Rodney joked. But Bradley took two strikes, setting up a thrilling 3-2 pitch.

"The first strike, you're like, 'OK, I can do it.' Then the second, and the third one is hard to throw," Rodney said. "I closed my eyes and threw it."