Both Hull and Thitikul reached the final green in two shots, with Thitikul putting her first putt inside six feet from the cup.
Hull missed her eagle chance, but Thitikul slid both her birdie attempt and her putt for par, which would have forced a play-off, past the hole.
Hull made no mistake from her own birdie chance to finish on 20 under overall and collect the $300,000 (£221,340) prize for victory.
Each carded a four-under 68 on the final round, giving Hull victory by the one-short margin she held after day three.
The 29-year-old, who had finished runner-up in her last two tournaments, held a two-stroke lead over Thitikul at the turn at TPC River’s Bend on Sunday.
Thitikul closed to within one on the 10th and both birdied the 11th, but Hull’s bogey at 13 allowed her rival to take the lead with a birdie at the next hole.
Hull responded with a birdie on the 16th but another bogey on 17 gave Thitikul the advantage she eventually squandered at the last.
Woad, 21, shot her best round of the week – a six-under 66 – on Sunday to finish on 18 under overall.