Weir had birdies on four of the first five holes. He was 13 under and ahead of Todd by two strokes when his tee shot at No. 5 settled 1½ feet from the cup. That came after Weir blindly hit out of a fairway bunker to 3 feet at No. 4.
But Weir missed the fairway and green for a bogey at the 431-yard sixth hole. At the same time Todd, who played the last 31 holes at TPC Four Seasons without a bogey, was tapping in at the fifth.
Todd rolled in a 17-foot par-saver at No. 17, keeping a two-stroke lead going to the final hole. He needed only 99 putts in the four rounds.
"It was a dream week for me on the golf course," Todd said. "Felt like I absolutely scored my pants off. It was just a short game display. I have a great short game, and even I'll say it was special this week."
Boo Weekley (68) was 9 under to tie for fifth with James Hahn (70). Weekley is the defending champion at Colonial, about 30 miles away and the next tournament.
Louis Oosthuizen, the 2010 British Open in the final group with Todd, had already slipped four strokes back at the turn before bogeys at Nos. 10-11. The 2010 British Open champion shot 74, 10 strokes worse than Saturday, to tie for 11th at 6 under.
Martin Kaymer won The Players Championship last weekend and opened at the Nelson with consecutive 67s. But he shot 71 Saturday before a bogey-birdie-bogey start Sunday on way to a 72 and tied for 29th at 3 under.
That was a stroke better than Jimmy Walker, who will remain No. 1 in the FedEx Cup standings.
Jordan Spieth, the 20-year-old Dallas native ranked eighth in the world, had a closing 68 to finish 2-under and tied for 37th at the tournament where he made the cut as an amateur at ages 16 and 17. He finished two strokes behind 17-year-old Scott Scheffler, the top junior golfer from Dallas who played on a sponsor exemption.