It was a repeat title for the world's top-ranked men's golfer. Woods, who claimed a winner's check of $990,000, shot 3-under 69 in the final round to finish at 20-under-par 268.
"A W's a W," he said.
Toms (67) and Villegas (67) tied for second at 19-under 269.
"Days like today are the reason I play the PGA Tour," said Toms. "To have a chance battling the best player in the world and going through all emotions --that's what makes it fun."
Fredrik Jacobson (68) was fourth at 15-under 273. Lucas Glover (69) and Tag Ridings (71) shared fifth at 14-under 274.