It was the 77th career PGA Tour event for Todd. He earned $1,242,000, a two-year PGA Tour exemption and a spot next year in the Masters.
Todd finished at 14-under 266. He took the lead for good with birdies at Nos. 9 and 10, and went on to become the eighth first-time winner this season.
Weir, the 2003 Masters champion who won the last of his eight PGA Tour titles in 2007, finished with a 67. Charles Howell III and Marc Leishman tied for third at 10 under.