Garcia couldn't do more than finish with six consecutive pars to end three shots behind, while Oosthuizen was left needing an eagle on the last to force a play-off.
Lee gave eventual victor Matt Kuchar a massive fight down the stretch at the Mexican event, but Kuchar just clung on to win by one shot at 22-under par, ahead of the charging Lee, who shot a final round six-under 65.
Matt Kuchar had gone four years, six months and three weeks since his last PGA Tour victory. "This is a high note".
Kuchar qualifies for the Sentry Tournament of Champions to start next year at Kapalua.
The last time Kuchar had a four-shot lead going into the final round was the 2014 Houston Open, and he wound up losing in a playoff when Matt Jones made a 45-foot birdie putt on the last hole and then chipped in from 40 yards in a playoff. Cameron Champ, the wunderkind PGA Tour rookie who captured the Sanderson Farms Championship recently for his first PGA Tour title, double bogeys the final hole but is still in contention in a tie for fifth at 14 under. He had another double bogey on the 17th hole and had to settle for a 69 to tie for 10th.
Westwood won back-to-back Nedbank titles in 2010-11, before the event was part of the tour, but hadn't tasted victory on the European Tour since April 2014.
Spaun's 66 earned him a share of third with Richy Werenski, while Garnett was a shot behind them on -18.More news: Family Photo! The Royals Pose for Prince Charles’ 70th Birthday
More news: United Kingdom says it has reached draft Brexit deal with EU
More news: Pakistan includes uncapped Shaheen Afridi in test squad
Kuchar is coming off a 2018 season that saw him record just four top-10s in 24 starts.
Rickie Fowler (68) and Tony Finau (65) are at eight under, along with their Ryder Cup captain, Jim Furyk, who had a 65.
He added Mayakoba at the last minute, and with his regular caddie having previous plans, Kuchar hired a local caddie from El Camaleon. Teryn Schaefer presents the best social media posts from around the world of golf in "Good, Bad & Unusual" and after each day's play brings you the biggest talking points in "The Takeaway".
The world number 133 has finished a shot behind American victor Matt Kuchar to earn one point one five million dollars and climb to 10th in the Fed Ex Cup standings.
To be exact, it was both guys' first win in 1,666 days.
Singh, who finished at 22-under 262, won for the third time this year and finished No. 4 in the Schwab Cup.