Joe Mauer doubled off the left-field wall with one out in the ninth against Chapman (4-4). Willingham followed with his 15th homer of the season, a 438-foot drive into the second level in left.
In Chapman's previous outing, he gave up a game-ending, two-run homer to Asdrubal Cabrera in the 10th inning at Cleveland last Tuesday.
Willingham's homer overcame Joey Votto's eighth-inning, two-run homer that had given the Reds a 3-2 lead.
Minnesota left-hander Scott Diamond (6-3), who'd lost his last two starts, allowed three runs and eight hits in eight innings. He struck out seven and also hit two batters, Votto and Brandon Phillips, with consecutive pitches in the third.
Former Reds pitcher Jared Burton worked the ninth for his first career save.
Reds starter Mike Leake allowed just five hits and no walks with five strikeouts in eight innings.
The loss left the NL Central leaders at 7-8 in interleague play this season and 104-131 all-time. The Twins finished 9-9 this year and are 157-125 all-time.
The Reds took a 1-0 lead in the fourth on Devin Mesoraco's leadoff double down the left-field line, Leake's sacrifice and Wilson Valdez's two-out single.
Trevor Plouffe tied the score with his 15th homer of the season, a 385-foot drive to right-center field with one out in the fifth. The shot extended to 62 the number of consecutive games in which at least one home run has been hit at Great American Ball Park, the longest current streak in the majors.
The score was 1-all when Mauer lined Leake's first pitch of the seventh to right field for a single and Willingham followed with a double, setting up Justin Morneau's RBI groundout.
Valdez led off the eighth inning with an infield single. Votto followed with his 14th homer of the season, an opposite-field drive to left.
NOTES: Minnesota closer Matt Capps, who'd been pitching with a sore shoulder, had what manager Ron Gardenhire described on Sunday as a ''setback.'' The right-hander will be examined on Monday after the Twins return from their road trip. The team was discussing possible roster moves, Gardenhire said. ... Minnesota definitely will add a pitcher as a 26th player for a scheduled doubleheader Saturday against Kansas City, Gardenhire said. Rules allow teams to add a player for scheduled doubleheaders. ... Minnesota CF Denard Span, hitless in his last 10 at-bats, did not start on Sunday. Ben Revere moved from right field to center. ... Reds SS Zack Cozart, who had one hit in 14 at-bats over his last three games, also got Sunday off. Valdez started in his place.