Toms, the 2003 and 2004 winner, caught fire on the back nine en route to a 7-under 63 to end at minus-13. Fred Funk finished alone in third place at 9-under-par 271 with Heath Slocum and Davis Love III ending one stroke further back at minus-8.
Leonard, who claimed his 10th PGA Tour win, played the front nine at plus-1 as he carded a lone bogey on the par-4 seventh on the TPC at Southwind.
Meanwhile, Toms was quietly making his move. He converted consecutive birdies from the third to move to minus-8. Around the turn, the LSU alum traded a birdie for a bogey from the 10th.
The gap Leonard owned continued to close as Toms birdied the 13th. Toms made it two in a row with a birdie on 14 to get within six strokes of Leonard.
Leonard, meanwhile, parred seven straight holes from the eighth. The 1997 British Open champion stumbled to a bogey on 15 to drop to 15 under.
Toms then caught fire. He eagled the par-5 16th to get within three. The 2001 PGA Championship winner inched within two shots as he chipped in for birdie on the 17th.
Toms could only par the last to end at minus-13.
'The first two days I was still getting used to the new greens,' Toms said. 'I think I had 23 putts on Saturday, so I started getting a feel for it. Then today, my short game got better and I started making putts. It just took me a little while to learn the golf course.'
Leonard parred 16 and 17. He then hit his tee shot into a fairway bunker at the 18th. Leonard's second shot ended in the rough right of the green. After taking a free drop away from the bleachers, he pitched onto the green. The 32-year-old two-putted for bogey and a one-shot win.
'I couldn't make a couple of putts that I needed to at 15 and 16, but I was glad to make that last one,' Leonard said. 'I did make some good putts on the front nine today, but I didn't play as aggressively as I wanted to.'
Toms, who missed the cut at this event three of his first four tries, has now finished in the top four in each of the last four years.
'It's just one of those things where I feel very comfortable off the tee and that's big for me,' said Toms of his good record here recently. 'It's big for my game when I get that feeling. For some reason, I feel good every day going to the golf course and feel good when I step on the first tee and that translates into good scores.'
A pair of Swedes - Richard S. Johnson and Fredrik Jacobson, shared sixth place at 7-under-par 273. Bob Estes, Neal Lancaster and Roland Thatcher ended one stroke further back at minus-6. Phillip Price took 11th place by himself at 5-under-par 275.