The double Open champion held off Sergio Garcia and Ben Curtis on a dramatic last day to end two shots clear at three under after a 66.
Garcia (68) and Curtis (71) finished one under after a tense three-way tussle during the latter stages.
Colombia's Camilo Villegas and Swede Henrik Stenson ended one over, while Steve Flesch was fifth at two over.
World number two Phil Mickelson and Argentine Andres Romero were four over and Scotland's Alastair Forsyth, England's Justin Rose, South Korea's Charlie Wi and India's Jeev Milkha Singh were tied ninth at five over.
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