''They've had their way with us,'' said Willingham, who played for the A's in 2011. ''If we would've come in here and lost today, that would've been a very big disappointment. We needed to get this win.''
Brian Dozier connected for his 20th homer in the first before Suzuki and Willingham 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.
Only 13-game losing streaks to the New York Yankees (2002-2003) and Texas Rangers (1998-1999) top the Twins' skid to Oakland.
''It's just one of those things,'' Suzuki said, struggling to find an explanation.
Phil Hughes (12-8) allowed four hits in seven innings for his second straight victory. He came out because of a cracked nail on his right index finger, which he glued back on in the clubhouse - something he said he has done throughout his career and shouldn't keep him from making his next start.
Stephen Vogt's RBI single in the first accounted for the A's only run. The poor offensive effort wasted a second straight superb start from Jason Hammel, who gave up four hits and one run in 6 1-3 innings.
Hammel, who beat Tampa Bay his last time out, had lost his first four starts with Oakland after being acquired in a July 4 trade with the Chicago Cubs that also sent Jeff Samardzija to the AL West leaders.
''This is the best he's pitched from what I've seen,'' A's manager Bob Melvin said.
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. But the biggest blunder might have been a self-inflicted one by the Twins.
Minnesota more than made up for the mistake in the eighth and ninth innings.
LOST IN THE SUN
Suzuki, who was a catcher for the A's from 2007-12 before returning for 15 games late last season, should know more than anybody on the Twins about how difficult the sun can be in Oakland during day games.
Instead, Suzuki provided one of Sunday's best bloopers when he never turned to catch Josh Reddick's popup that bounced off the warning track behind the plate in the fourth. Reddick drew Oakland's only walk off Hughes in the at-bat.
''They said I missed it. But I didn't think I missed it because I didn't even try to go for it,'' Suzuki joked. ''It doesn't count as a miss.''
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.