The result means the USA have still not won on European soil in 25 years, their troubles summed up by Tiger Woods' 0-4 record this weekend.
Thomas Bjorn's side had to hold off a fightback from the visitors, who at one point cut the gap to a solitary point, but reached the 14.5 points needed to secure the victory courtesy of Open champion Molinari's 4 and 2 win over Phil Mickelson.
The Italian became the first European player to finish with a 5-0 record, having won four matches alongside Tommy Fleetwood.
