Simpson was trying to become the first player to win three times on the PGA Tour this year, but even though he lost to Crane in the playoff he took over the money lead from world No. 1 Luke Donald.
Crane and Simpson tied at 15-under-par 265 after Crane shot a fourth round 63 over the Sea Island Resort's Seaside Course. Simpson fired a 66.
Both players passed third-round leader Michael Thompson, who hit his tee shot into a hazard at the closing hole and suffered a bogey that left him one shot out of the playoff. Thompson shot a 69 for his 266 total and Louis Oosthuizen was alone in fourth at 267.
Crane and Simpson both made a par on the first playoff hole, the par-4 18th, but Simpson suffered a bogey at the par-3 17th, which was the second extra hole.
It was Crane's fourth PGA Tour victory.
Simpson won $432,000 for his second-place finish and that gives him $6,200,243 for the year. Donald, who did not play this week, has won $5,837,214 on the American tour. Both will be in action next week at the season-ending tournament at Walt Disney World and will battle for the money title.
Donald is trying to become the first player to finish first on the money list in both the United States and Europe in the same year.
Bud Cauley, who turned pro in June at the age of 21, shot a 66 Sunday and finished tied for 15th. He thus clinched a position among the top 125 players on the money list this year and becomes the sixth player to earn a PGA Tour exemption without having to go through the qualifying tournament.