Pat Perez (70), David Gossett (71) and Loren Roberts (71) finished tied for second at 10-under-par 274.
'Honestly, I can't describe it,' said Smith. 'It's been unbelievable.'
Smith took the 36-hole lead for the first time in his career with a round of 67 Saturday. On Sunday, Smith had to hold off several challengers on the West Course at Westchester Country Club.
Smith had an up and down start and opened with a 10-foot birdie at the first to reach 12-under. At the very next hole, Smith three-putted for bogey but recovered with a birdie at No. 3.
Roberts stepped up and grabbed a share of the lead with a birdie at the sixth. However, Roberts made back-to-back bogeys from the seventh to see his chances at a comeback dwindle.
Smith bogeyed the fifth but kept plugging along and opened a two-shot edge over the rest of the field at the par-4 10th. He chipped up onto the green inside 18 feet of the cup after a long drive and then drained the putt to return to minus 12.
Smith saved par at the 11th after an errant drive nearly landed in a ditch. At the 12th, Smith continued to struggle off the tee and missed the fairway en route to a bogey.
'I had trouble all week,' said Smith. 'I had a hard time getting in the fairway and hit my drive in the left rough.'
Gossett was also in the middle of a roller coaster round and moved into a tie for first with a birdie at the 14th. At the very next hole, Gossett found the rough to the left of the green. He had an awkward lie and hit his third shot short into a bunker. The 23-year-old managed to get up and down for bogey to fall out of a share of the lead.
Perez, who squandered a late lead at the Pebble Beach Pro-Am in February, was intent on making up for the early-season blunder. At the par-3 16th, Perez chipped in for birdie from just off the green for a share of first.
Smith, who heard the roar of the gallery from the 15th, responded moments later. He hit a brilliant second shot onto the putting surface within 20 feet of the hole and then ran home the putt for birdie and the outright lead at 12-under.
Smith cruised at even par to finish the round. He had a long birdie try at the par-5 18th after he hit his third shot onto the green and watched as the ball skimmed the cup. Smith threw his hands in the air, but his win was already secure. He converted the short par putt for the title.
The 32-year-old collected $630,000 for the win but he will not be able to carry his momentum into next week's U.S. Open at Bethpage State Park's Black Course.
'Obviously you want to play in the Open,' said Smith. 'I've played six weeks in a row and I'll probably be teeing it up on Thursday and Friday with my two kids. There's probably not a better group than playing with them.'
Stewart Cink birdied three of the last four holes for a round of 3-under 68. Cink finished tied for fifth alongside Ian Leggatt at 9-under-par 275.
Tom Lehman also carded a 3-under-par 68. He was joined by Jerry Kelly at 8-under-par 276.
Jim Furyk, Peter Lonard and Stephen Ames were tied for ninth at 6-under-par 278.
A total of six players finished tied for 12th at 5-under-par 279, including last year's winner Sergio Garcia and Bryce Molder.
For Molder, the result was worth so much more. The 23-year-old earned $66,500 to become eligible to receive sponsor's exemptions for the rest of the season.
He was joined by Len Mattiace, Mike Weir, Brad Faxon and David Toms seven shots off the lead
Final results from the Buick Classic