MINNEAPOLIS — After all the talk of the Twins’ inability to go toe-to-toe with the big boys of the league this season, they took the opportunity to flip the script.

The Phillies came to town with, by far, the best record in baseball, but the Twins scraped together three gritty games to claim the series, capping the effort in style with Max Kepler’s walk-off infield single that sealed a 5-4 victory at Target Field on Wednesday in front of an energetic crowd of 33,813.

It marked Kepler’s 11th career walk-off plate appearance, tying him for the most in Twins history with Hall of Famers Kirby Puckett and Harmon Killebrew. He’d also picked up his 500th career RBI earlier in the game (and added No. 501 on the walk-off), making him the 12th player in Twins history to pick up 500 RBIs with the club.

“Great company to be next to the big dogs like that,” Kepler said. “But I’ve got to keep a small dog mentality. Stay hungry and keep working.”

And speaking of big dogs, the Twins took this series without three of their biggest offensive threats — Carlos Correa, Royce Lewis and Jose Miranda — of which the latter two could be expected back for this weekend’s series at Comerica Park against the Tigers.

After another afternoon of mostly missed opportunities on offense, the Twins finally broke through in the seventh inning, when they at last took advantage of a bases-loaded situation with a Kepler RBI groundout. Carlos Santana delivered the breakthrough knock with a double to the left-field wall that brought home two more runners to tie the game.

Trevor Larnach led off the ninth with a hit-by-pitch, moved to second on a wild pitch and to third on a sacrifice bunt, then touched the plate when Kepler again simply put the ball in play toward second baseman Bryson Stott for the Twins’ fifth walk-off victory of the season.

“There’s a lot of scenarios where that ball, even though it’s not hit hard, becomes productive,” manager Rocco Baldelli said. “And I was glad the way that we came together these last three days against a really good team. Nobody let up. Nobody ever quits here, and the guys continue to play hard until we get the win.”

Strong pitching from the back end of the rotation was the underpinning of the series victory, with Bailey Ober, Simeon Woods Richardson and David Festa (the bulk pitcher behind the opener on Wednesday) combining to allow three runs over 17 1/3 innings to keep the Twins neck-and-neck with the Phillies.

Even as the Twins likely pursue another starter ahead of Tuesday’s Trade Deadline, the starting pitching depth has at least shown the upside in the ability to neutralize a lineup like that of the Phillies.

Ober held them at bay for seven innings of two-run ball on Monday as the Minnesota offense took off, followed by the best start of Woods Richardson’s career (six scoreless frames) on Tuesday, when the Twins and Phillies took a scoreless tie into the ninth inning before the Minnesota bullpen faltered.

And perhaps most impressively, Festa, the organization’s top pitching prospect, shrugged off not only two tough outings to begin his MLB career, but also two inherited runners from opener Steven Okert with one out in the first inning, to strike out a career-high seven batters while holding the Phils to one run over 4 1/3 frames on Wednesday.

“We did it with excellent pitching,” Baldelli said. “It’s just good baseball. If you enjoy watching good baseball, I think this series was a good example of what you’re looking for.”

Though the Twins did enter the series with a 2-19 record against teams with better records than them following their sweep at the hands of the Brewers in a two-game series over the weekend, even the banged-up version of this group had more than enough steam to not only keep up with an elite squad, but also to best them.

Following that second Milwaukee loss, Baldelli said his team simply needed to find execution in the big moments against the big opponents — and his team delivered.

“We’re grinding with what we have,” Kepler said. “A lot of guys are down on the injured list, and we’re still competing, which is special with a group this young right now, to go through the stuff we’re going through against these top-tier teams. It’s special.”