The U.S team was trailing 10-6 going into the final singles matches at the Golf Club St. Leon-Rot in Germany but eventually won 14 1/2 points to 13 1/2 points.
Caroline Masson had a putt to retain the trophy for Europe but she missed and Gerina Piller sank a nine-footer to claim a decisive victory for the Americans.
With Lizette Salas, Angela Stanford, Cristie Kerr, Michelle Wie and Paula Creamer, who won the clinching point, taking the bottom five singles it was a stunning turn around.
But the conclusion to the biennial team event will be remembered for an incident in the morning fourball matches.
In the final grouping, Alison Bell of the U.S. had a birdie putt on the 17th to pull herself and Brittany Lincicombe one hole clear of Suzann Pettersen and Charley Hull.
She missed it to within a few inches from the hole and believing it to be conceded picked the ball up as all four players began walking to the 18th tee, with the umpire announcing the match was still all square.
However, Norway's Pettersen then claimed she had not conceded the putt and the umpire awarded the hole to Europe by forfeit.
It mattered little that the European pair took the final hole to win two up, as a bitter row broke out.
Hull, who appeared to disagree with her teammate's action, was left in floods of tears as was Lee, who believed she had cost her team the chance of victory, then trailing by four points.
U.S. captain Juli Inkster was furious and did not mince her words: "It puts a damper on the whole thing. No way they can ever justify that. It's just not right. I don't care what they say. You just don't do that to your peers.
"I have never seen anything like it in my career. It's disrespectful."
Laura Davies, who has played 12 Solheim Cups for Europe, also condemned Pettersen.
"I'm disgusted," Davies told Sky Sports.
"How Suzann can justify that I will never, ever know. We are all fierce competitors but ultimately it's unfair. We have to play week in, week out together and you do not do something like that to a fellow pro.
"She has let herself down and she has certainly let her team down."
Europe captain Carin Koch defended Pettersen, saying her actions had been "within the rules of golf" but admitted it may have fired up the U.S. team.
Europe needed just three and a half points from the 12 singles matches to retain the trophy, but fell short as the U.S was not to be denied its first win in the event since 2009.
Lee beat Gwladys Nocera 3-1 before Piller's gutsy heroics on the 18th denied Europe and set up the U.S. triumph as the scoreboard turned a sea of red, denoting American wins.