"Overall, it was a good series," Twins manager Ron Gardenhire said. "We sure wanted to try to finish it off. I sure like the fact that our guys were still getting after it in the last inning there and trying to find a way. That's pretty much the way the whole series went; our guys battled hard. We're excited about that part of it."
Willingham was the first to go deep in the ninth, crushing his team-leading 28th homer to lead off the inning against Vicente Padilla. And after Justin Morneau walked, Doumit hit his 11th homer to bring the Twins to within two runs.
But closer Alfredo Aceves, who blew the save on Saturday, came in and got three quick outs to give the Twins just their third loss over their last 10 games.
"After last night's game, coming from behind when everyone counted us out gives us confidence that no lead is safe with us," Doumit said. "Today was just another example. We fell short, but we didn't go down without a fight."
Right-hander Nick Blackburn took the loss, as the sinkerballer gave up four runs on nine hits over five innings.
The Red Sox struck first with two runs in the third, with Carl Crawford bringing home a run on an RBI groundout before Adrian Gonzalez contributed an RBI single.
Gonzalez added a two-run homer in the fifth inning over the Green Monster to score Crawford with two outs. It was Gonzalez's 11th of the year and came on a 2-1 sinker. Blackburn has had trouble keeping the ball in the park, as it was his team-leading 18th homer given up this year.
But the 30-year-old, who entered with a 7.43 ERA, said he was mostly satisfied with his outing other than the homer from Gonzalez.
"I wouldn't say today was a step back by any means," Blackburn said. "I had location. I threw a lot of pitches I was very pleased with. [I threw] glove-side sinkers, got those lefties to freeze up a couple times. There's going to be games where you go out and one pitch beats you, and today was one of those days."
Minnesota got on the board in the fifth on a sacrifice fly from Ben Revere to score Alexi Casilla, who walked, stole second base and advanced to third on a groundout from Jamey Carroll.
But it was all the Twins could do against left-hander Franklin Morales, who allowed just one run on three hits and three walks over six innings.
The Red Sox added an insurance run in the seventh against reliever Jeff Manship on an RBI single from Cody Ross. But Revere saved the Twins from any further damage with an over-the-shoulder catch in center field to end the inning with a double play. Jacoby Ellsbury contributed a sacrifice fly in the eighth to finish the scoring for Boston.
"Spectacular," Red Sox manager Bobby Valentine said about Revere's catch. "Absolutely. Ken Griffey, Willie Mays. As good as it gets. That ball is not caught often, and we saw it here today. Terrific catch."
Those two runs loomed large with the Twins rallying in the ninth inning before ultimately coming up short. It was still Minnesota's first series win in Boston since 2006.
"I'll take that every year," Doumit said. "Coming in here and taking two of three or three or four from the Red Sox. We feel good about this series. So I'll take three of four every time."