Thanks to Jim Thome’s bat and Ken Griffey Jr.’s arm, the AL Central has a winner at last: the Chicago White Sox.

John Danks pitched eight innings of two-hit ball on short rest, Thome homered and Griffey threw out a runner at the plate with a tough tag by A.J. Pierzynski, helping Chicago beat the Minnesota Twins 1-0 in a 163rd-game tiebreaker for the division title Tuesday night.

The White Sox joined the crosstown Cubs in the postseason, the first time since 1906 that both Chicago teams made it. And just as the Cubs did when they clinched the NL Central crown, several White Sox players came back on the field after the final out and sprayed fans with champagne.

Next up for the South Siders, a first-round matchup with the surprising Rays. Game 1 is Thursday at Tampa Bay, which won the AL East.

‘‘Look at this,’’ Thome said with the crowd roaring all around him. ‘‘This is what it’s all about — October baseball.’’

The White Sox got a huge boost Tuesday from two of their oldest players: Thome and Griffey, both seeking their first World Series championship.

Thome’s long drive on a 2-2 pitch from rookie Nick Blackburn cleared two rows of shrubs in center field, traveling an estimated 461 feet to snap a scoreless tie in the seventh. It was the 541st homer for Thome, who raised his right fist as he rounded first base. He hadn’t been to the playoffs since 2001 with Cleveland.

Griffey, who came to the White Sox in a trade with the Reds so he could have a chance at playing in the postseason, cut down Michael Cuddyer with a nice throw from center in the fifth. Griffey, who like Thome is 38, will be making his first postseason appearance since 1997 with Seattle.