The defending champions looked set to suffer a crushing defeat when the Americans took control of three of the four matches entering the final stretch.
But the series ended with the home side not managing one full point.
The ice cool pair of Catriona Matthew and Carin Koch set the tone in the first match.
Two down with four to play against teenage sensation Paula Creamer and the experienced Beth Daniel, they won the 15th and 17th to sneak half a point.
Trish Johnson and Sophie Gustafson were three down with four to play against Pat Hurst and rookie Christine Kim, but then won three holes in a row - the 15th and 17th with birdies - and salvaged a half point with a par at the last.
But the biggest turnaround of all came in the final match. World number one Annika Sorenstam and Suzann Pettersen were four down after 12 holes to Michele Redman and the five months pregnant Laura Diaz.
But Sorenstam then produced the form which has made her such a dominant player in the women’s game when she lipped out for a hole-in-one at the 13th.
The easy tap-in set up a run of four birdies in five holes for an amazing one hole victory.
The powerful pairing of Laura Davies and Maria Hjorth put the first point on the board for Europe with a relatively comfortable two and one win over the American number one Cristie Kerr and Natalie Gulbis.
Pettersen, a controversial captain’s pick after spending eight months out of the game with a back injury, typified the European fire by holing big putts for birdie at the 16th and 17th.
The win raised memories of Barseback in Sweden two years ago when Pettersen and Sorenstam produced a fighting win over Diaz and Kelly Robbins in the Saturday fourballs and paved the way for a European victory.
“It just shows how you should never give up,” said Sorenstam. “We made a couple of birdies and suddenly the momentum swung in our favour.”
The scoreline maintained Europe’s traditional strength in the foursome format. It is the fourth set of matches in a row which Europe has led after the opening series.