Slattery double-bogeyed the final hole but managed to finish with a 1-under 71, good for final tally of 15-under 273 and a one-stroke win over Lorenzo Gagli.
The Briton put his third shot on No. 18 into a water hazard off the green at El Encin Golf Hotel. He chipped to about 11 feet with his fifth and then two-putted for a narrow victory.
Gagli (70) could have forced a playoff but came up short on a birdie putt, ending at 14-under 272.
Cesar Monasterio, who held the lead for a time Sunday, posted three bogeys on the back nine and tumbled to 1-under 71, good for a third-place tie with Eduardo de la Riva (70) at minus-12.
Defending champ and world No. 1 Luke Donald registered an even-par 72, ending in a tie for 11th at 8-under 280.