Karlsson and Stenson, four strokes behind the Spaniards after the third round, finished at 27-under 261 on Mission Hills Olazabal Course.
I thought it was our turn today, Stenson said.
Swedens only other victory in the event came in 1991 when Per-Ulrik Johansson and Anders Forsbrand beat Wales by a stroke at Le Querce in Rome.
Jimenez and Larrazabal finished with a 70 in their bid to give Spain its fifth title and first since 1984. Australias Richard Green and Brendan Jones (76) and Japans Ryuji Imada and Toru Taniguchi (68) tied for third at 18 under. Americans Ben Curtis and Brandt Snedeker (73) finished ninth, 14 strokes back at 13 under.
The victory caps a great season for Karlsson, a two-time winner on the European Tour. Stenson is winless this season in individual play.
Im starting to run out of tournaments, Stenson said. This is my third last. So, Ive got two more to go in South Africa. But winning for Sweden in nice. Its been a while.
The Swedes made five brides on the front nine to catch the Spaniards at 23 under. Playing a group ahead of Spain, Stenson missed a short birdie putt on 10 that would have put them at 24 under.
Sweden pulled into the outright lead with birdies on Nos. 11, 12, 14 and 15 to reach 27 under ' four clear of Spain. Stenson missed a 10-footer on No. 13 that would have extended the lead even more.
The key was mastering the difficult foursomes (alternate shot) format, played Friday and Sunday. In foursomes, teams play only one ball and alternate shots. Fourballs (best ball) is easier. Each golfer plays his own ball and counts the best score on each hole.
Sweden shot 67-63-130 playing foursomes and 65-66-131 playing fourball.
The Swedes were the favorites entering the tournament, and two of only three players in the field ranked in the top 20. Karlsson, who won the European money title this season, is No. 6 and Stenson 12th. Spains Jimenez is ranked 20th.
All four days were played in perfect conditions with a light breeze stirring through the hilly, tree-lined course designed by two-time Masters champion Jose Maria Olazabal. The rolling layout would look familiar anywhere. Only a 100-foot-high stone statue of Guanyin along the 18th fairway ' a Chinese female goddess with Buddhist origins ' suggests the clubs location.
The Swedes split $1.7 million in prize money, a big chunk of the $5.5 million purse. Despite the global economic downturn, the purse offered by sponsor Omega was 10 percent above last year. This years event was the second of a 12-year contract at Mission Hills, the sprawling golf estate that boasts the worlds largest layout with 216 holes.