Parker, who gave up seven hits with two walks and four strikeouts in six innings, hasn't lost a decision since May 22, a span of 19 games. But that was of little consolation to the 24-year-old Norwell graduate..
“I'm not happy that we lost, no matter what,” Parker said. “Got to move on.”
Parker also gave up a homer to Oswaldo Arcia, who helped Minnesota snap Oakland's three-game winning streak and prevented the A's from stretching their two-game lead over Texas in the AL West. The Rangers lost to Pittsburgh, 5-4.
Despite giving up the homers to Willingham and Arcia, Parker appeared to be on the verge of earning his 12th win. But Arcia singled off reliever Sean Doolittle to lead off the eighth. Doolittle struck out Ryan Doumit before being pulled for Cook (6-4), and Willingham followed by launching a 2-0 pitch an estimated 439 feet into the middle deck for his second multi-homer game this season.
It was only the second homer Cook had given up all year.
Willingham hadn't homered since Aug. 13 and entered the game hitless in his last 15 at-bats. Normally accustomed to batting cleanup as Minnesota's designated hitter, Willingham batted sixth and played left field Tuesday.
Anthony Swarzak (2-2) pitched a scoreless eighth to pick up the win on his 28th birthday, and Glen Perkins pitched the ninth for his 34th save in 38 chances.
Twins starter Liam Hendriks worked 51/3 innings and matched his career high with six strikeouts. He had a one-run lead for most of those innings thanks to Willingham's second-inning solo shot.
“He likes playing against the teams he used to play for,” a grinning Hendriks said of Willingham, who played a season with Oakland.
The A's took a 2-1 lead when Alberto Callaspo sent a 1-1 pitch 384 feet into the right-field seats after Hendriks hit Yoenis Cespedes to lead off the fifth. Hendriks hit Brandon Moss the next inning and Cespedes followed with a run-scoring single to put Oakland up 3-1.
Parker got into trouble in the sixth after Arcia led off with a monster homer to right. Three of Minnesota's next four batters reached to load the bases for Pedro Florimon. But after a meeting on the mound, A's manager Bob Melvin elected to leave Parker in the game, and he calmly induced Florimon into a double play to end the threat.