Ben Revere and Jamey Carroll each had three hits and two RBIs and Josh Willingham also homered for the Twins, who have won 10 of 13 games.
Jimmy Rollins had four hits and two RBIs for the Phillies, who left 10 runners on base and couldn't overcome another poor start from Kyle Kendrick (2-6). The right-hander gave up six runs on eight hits with two walks and two strikeouts. He has a 7.80 ERA in his last three starts.
The injury-plagued Phillies fell to 29-34, 9½ games behind Washington in the NL East.
Joe Mauer added two hits and two RBIs for the Twins, who scored at least 10 runs for the third time in seven games, got up big early and then kept turning the Phillies back every time they started to close the gap.
Span started the Twins first inning with a home run to right field, his second of the season and fifth career leadoff homer.
The Twins tacked on four more in the second inning on Plouffe's two-run homer and base hits from Revere and Mauer to take a commanding 5-0 lead.
But the Phillies started chipping away, scoring four off Nick Blackburn (3-4) in the fourth inning, stringing three straight hits together to get the rally going. Rollins was in the middle of everything, starting the game with a single, picking up doubles in the third and fourth and getting a single and scoring on a base hit from Jim Thome, the slugger who reached the 600-homer plateau in a Twins uniform, in the sixth to cut Minnesota's lead to 8-7.
Willingham hit a solo home off of lefty Joe Savery in the sixth and Carroll drove in Plouffe with a single in the seventh for a little more breathing room.
The epitome of the Phillies' hard-luck season may have come in the seventh when the Twins had two on and two out and Revere at the plate. Revere popped a foul ball up along the third base line and Phillies third baseman Mike Fontenot gave chase.
Just as he was about to haul in the final out, a young boy reached up with his glove and snatched it away. The youngster was wearing a Phillies cap and Phillies jersey. Given new life, Revere poked a single through the right side of the infield to score Span to make it 11-7.
The offensive outburst helped the Twins overcome a shaky start from Blackburn, who lasted five innings. The right-hander gave up four runs on eight hits with two walks and a strikeout in his second start since coming off the disabled list.
NOTES: Willingham tipped his cap to his wife, Ginger, after crossing home plate in the sixth. Ginger tweeted that it was her birthday and she asked her hubby for a homer. ... Mauer picked up his 500th career walk in the seventh. ... Phillies 2B Chase Utley (knee) started a rehab assignment with Class-A Clearwater on Tuesday night. ... Phillies manager Charlie Manuel came out to argue with 2B umpire Manny Gonzalez in the fifth inning that Plouffe missed third base while scoring on a double from Carroll. ... The Twins held a moment of silence for former RHP Dave Boswell, who died at his home in Maryland on Monday. ... P.J. Walters (2-1, 4.42) will take the mound for Minnesota on Wednesday in Game 2 of the series against Phillies LHP Cole Hamels (8-3, 2.93).