Europe leads 5 -4 at the 6,983-yard, par-72 Saint-Nom-la-Breteche Golf Club outside of Paris.
A six-foot birdie from Jamieson secured their win on the final hole after the Italians had been one up with two holes to play.
"The golf that was played was beautiful," B&I captain Sam Torrance said.
But B&I could even have finished the day all square with Europe as Fleetwood and Wood fought back strongly from 3 down after 14 holes.
Wood's eagle on the 17th ensured it went to the final hole, where both he and Fleetwood had putts to halve the match, but missed.
Lawrie expressed his disappointment last week that eight of his Ryder Cup teammates snubbed the tournament.
Justin Rose, Rory McIlroy, Graeme McDowell, Luke Donald, Lee Westwood and Ian Poulter aren't playing despite being B&I's six leading qualifiers. Sergio Garcia and Peter Hansen declined places in the Europe team.
The Seve Trophy, which is played in non-Ryder Cup years, is named after the late Seve Ballesteros, who died in 2011.