NEW YORK — Aggressive base-running, several Yankees gaffes and some stalwart relief pitching propelled the underdog Minnesota Twins to a 3-1 win over New York in game one of their best-of-five AL division series Tuesday.

The teams meet again Thursday night in New York.

It was the Twins’ first win over the Yankees in 14 tries, dating back to May 2001.

Speedy Cristian Guzman set the tone in the third frame when he challenged the arms of both Hideki Matsui and Bernie Williams to plate the game’s first run.

Guzman raced from first to third on Shannon Stewart’s single off Yankee starter Mike Mussina (17-8), catching Matsui off guard with his daring.

The rookie leftfielder’s throw to Aaron Boone at third was a little late. Guzman then scampered home when Luis Rivas flied to Williams in shallow center.

The Twins added two more runs in the sixth inning, with Williams playing a part again.

With designated hitter Matt LeCroy aboard, Williams misplayed Torii Hunter’s liner, the ball skipping by him.

LeCroy came around to score with Hunter following him home after Alfonso Soriano tried to gun him down in a dash for third.

Soriano’s throw sailed well over Boone’s head. Twins starter Johan Santana (12-3) was long gone by that time, sitting down with leg cramps after just four frames.

He was replaced by 39-year-old right-hander Rick Reed, a move that had Yankee fans cheering.

Undaunted, Reed retired two batters before giving way to JC Romero, who worked one and one-third innings.

LaTroy Hawkins then came on to snuff out a Yankee threat in the seventh. The hosts put two men on with none out but could not capitalize.

Eddie Guardado closed out for the Twins, working a nervous ninth. He allowed three hits but just one run, with Williams scoring on Soriano’s infield single.

Stewart bailed him out with a spectacular leaping catch that appeared to be headed over the fence.