The Mets and Phillies both beefed up their bullpens Wednesday.

Philadelphia then struck first in the battle to upgrade their outfield.

The Phillies acquired Twins center fielder Harrison Bader — who played for both the Mets and Yankees in the past — for a pair of prospects, The Post’s Jon Heyman confirmed.

Minnesota is receiving outfield prospect Hendry Mendez and minor league righty Geremy Villoria, according to The Athletic.

The Phillies trail the Mets by a half-game in the NL East and both teams aim to claim the division and potentially a first-round bye.

The Mets added Ryan Helsley and Tyler Rogers on Wednesday, while the Phillies countered by acquiring Twins closer Jhoan Duran.

Both teams are rumored to be hunting for center field help, with Bader, the White Sox’s Luis Robert Jr. and the Orioles’ Cedric Mullins mentioned as possible.

The Phillies, after giving up a big package for Duran, opted for the Bronxville, N.Y. native who is having his best offensive season in four years.

Bader, 31, is slashing .258/.339/.439 with a .778 OPS, while adding 12 homers and 38 RBIS. He’s also tallied 10 stolen bases.

His 111 OPS+ entering the day is his highest since he notched a 114 mark in 2021.

Bader is best known for his glove, having won a Gold Glove in 2021, and he has a plus-13 defensive runs saved rating and plus-five outs above average mark, according to Fangraphs.

The Phillies used Johan Rojas in center field in Wednesday’s 9-3 loss, and it’s logical to expect Rojas would now shift to a bench role.

Philadelphia has a 4 1/2-game lead over the Reds for the third and final NL wild-card spot, and host the AL-leading Tigers in a three-game set beginning Friday.

The Mets instead welcome the Giants, from whom they acquired Rogers, for a three-game set starting Friday.

The teams met last weekend in San Francisco and the Mets secured a three-game sweep.