Brian Dozier connected for his 20th homer in the first before Suzuki and Willingham — both former A's players — each had a big hit against Luke Gregerson (2-2) in the eighth. Minnesota scored two more in the ninth to avoid a four-game sweep with its first win over the A's since last September.
Phil Hughes (12-8) allowed four hits in seven innings for his second straight victory. Stephen Vogt's RBI single in the first accounted for the A's only run.
Jason Hammel gave up four hits and one run in 6 1-3 innings for Oakland.
Coco Crisp and Josh Donaldson singled in the eighth before Casey Fien struck out Brandon Moss and got Vogt to fly out to center to end the A's best chance to rally.
After they each allowed a run in the first, Hammel and Hughes quickly corrected most of the mistakes they made the rest of the way.
The biggest blunder might have been a self-inflicted one by the Twins. With two runners on in the seventh, Minnesota messed up a squeeze attempt when Jordan Schafer whiffed at a bunt and Eduardo Nunez was tagged out between third and home. Fernando Abad struck out Schafer on the next pitch.
Minnesota more than made up for the mistake its next time up.
Danny Santana singled leading off the eighth, stole second and advanced to third on Gregerson's wild pitch. Dozier flied out to center before Suzuki doubled and Willingham went deep for the 12th time this season.
Suzuki, who was with the A's from 2007-12 before returning for 15 games late last season, drove in another run in the ninth on a swinging bunt against Jesse Chavez. Willingham played for Oakland in 2011.
Twins: First baseman Joe Mauer, who has been out since July 1 with a strained muscle on his right side, is expected to be activated at Houston on Monday. Infielder Trevor Plouffe (sore left foot) and outfielder Oswaldo Arcia (lower back pain) sat out. Both are day to day.
Athletics: Shortstop Jed Lowrie got the day off to rest his bruised right index finger, which sidelined him for three games last week. He's expected to start Monday at Kansas City.
Twins: Minnesota will call up former A's lefty Tommy Milone from Triple-A Rochester to start Monday in Houston. Milone was dealt to the Twins at the July 31 trade deadline for outfielder Sam Fuld after going 6-3 with a 3.55 ERA for Oakland this season.
Athletics: Sonny Gray (12-5, 2.87 ERA), the AL Pitcher of the Month for July, tries to rebound from back-to-back losses in August when he goes in the opener at Kansas City.