The 33-year-old from Southport, who was also looking to secure his playing status for next year, held a three-stroke lead over Italian Lorenzo Gagli heading up the 18th but put his third shot into the water.
He gathered himself again, though, pitching his fifth to within 15 feet and then two-putted for a double bogey to finish on 15 under par, one better than Gagli.
Eduardo De La Riva and Cesar Monasterio finished a further two shots back on 12 under.
Slattery held a two-shot lead overnight but saw that advantage wiped out as he stumbled out of the blocks in the final round, bogeying the third and fifth holes.
A birdie on the seventh steadied the nerves and he went on to pick up further shots on 11, 13, 14 and 15 before his final hole wobbles frayed the nerves as he closed with a one-under 71.
He admitted he was trembling even as he stood over the short putt he had to claim the crown.
"I had a two-footer on the last to win and I have never shaken so much in my life," he told Sky Sports 2.
"I was so relaxed on the back nine, making birdies, but as soon as I made a mistake, like I did on the last, it became quite tough.
"It was nerve-wracking."
Slattery, ranked 136th in Europe and previously in danger of losing his Tour card after missing six cuts at his last 11 events, is hoping the win at El Encin Golf Hotel will revitalise his career.
"It's more the belief," he said. "I have been out here for seven years and now I believe I can win.
"People have been telling me for years I can win and now I believe it.
"That has been the biggest problem and this (win) for me is huge."
Gagli and Argentinian veteran Monasterio led at the turn and the former even had a birdie chance on the last to take it to a play-off.
But even though it slid past it should not detract from another excellent week for Gagli.
The 25-year-old has been enjoying a promising season on the European Tour and represented a fifth top-five finish.
He was two-under through nine but another birdie at 11 was offset by a bogey on 14 as he failed to capitalise on Slattery's closing struggles.
Australian Brett Rumford, second alongside Gagli overnight, fell away with a final round 77 while world number one Luke Donald shot an even-par 72 to finish eight under, seven adrift.