One stroke behind going into the fifth and final round, Haas fired a flawless eight-under-par 64 to break clear of a congested leaderboard in the pro-am celebrity event.
The 27-year-old two-putted for birdie from long range on the 18th green for a 30-under total of 330 to emulate his father Jay Haas, Bob Hope champion in 1988.
PGA Tour rookie Alex Prugh, co-leader overnight with the long-hitting Watson, birdied the last three holes for a 67 and fifth place at 28 under.
Haas, who had never previously finished higher than joint third on the PGA Tour, was delighted to triumph after weathering a bout of nerves over the closing stretch.
"This feels unbelievable," he said in a greenside interview, where he was joined by his father Jay, who flew in from Hawaii earlier in the day, and his great uncle Bob Goalby, the 1968 Masters champion.
"I was so nervous coming down the stretch. I still don't know how I hit the shot on 18 -- my hands were shaking," Haas said of his approach at the last.
"I told my caddie on the last hole: 'I am as nervous as hell.' And he said: 'Well, that's a good thing.'"
A fifth-round birdie slugfest was always on the cards with 14 players bunched within five shots of the overnight lead and Haas and Kuchar made the most significant early moves.
Haas briefly moved two shots in front with four birdies in the first six holes before reaching the turn tied for the lead with Kuchar, who had surged to seven under for the round after 10 holes.
Another birdie followed for Kuchar at the par-five 11th, where he reached the green in two and two-putted, to put him one stroke clear.
Haas, playing two groups behind Kuchar, failed to birdie the 11th but he sank an 18-footer to birdie the par-five 14th and regain a share of the lead.
Clark then made it a three-way logjam at the top when he knocked in a six-foot putt at the par-three 15th for his sixth birdie of the round.
Kuchar again snatched the outright lead, coaxing in a 16-foot birdie putt at the par-three 17th before thrusting his right arm skywards in celebration.
Moments later, though, Clark drew level with a matching birdie at 17, a curling 20-footer lifting him to 29 under par.
Haas also birdied 17 after hitting an exquisite tee shot to seven feet to join Clark and Kuchar in a tie for the lead.
Kuchar's birdie attempt from 13 feet at the last slid past the right edge of the cup and Clark's miss there soon after left the way clear for Haas to take advantage.
(Writing by Mark Lamport-Stokes, editing by Nick Mulvenney)