Simpson, who won the 1987 U.S. Open at Olympic Club, closed with a 4-under 68 to end at 12-under-par 204.
Massy Kuramoto ended alone in fourth at 10-under-par 206 thanks to a 7-under 65. Second-round leader Tom Kite and JELD-WEN Tradition winner Eduardo Romero were one stroke further back at minus-9.
This event paired Champions Tour players with junior golfers from The First Tee program, as well as other amateurs. The event used two golf courses -- Pebble Beach Golf Links and Del Monte Golf Course -- for the first two rounds, while Pebble Beach hosted the final round.
Haas flew into the lead early on. He ran off three straight birdies from the second to jump to minus-12. He gave a stroke back on five, but came right back to birdie the sixth, then parred the next four holes.
Simpson sank back-to-back birdies from the fifth to get to 10-under. Playing two groups ahead of Haas, Simpson birdied the 11th to get to 11-under.
Haas three-putted for bogey on 11 to create a four-way tie for the lead with Simpson, Edwards and Dan Pohl. Simpson remained steady as he parred his next six.
The 52-year-old Haas moved one ahead of the pack with a birdie at the par-5 14th. He could not save par from a greenside bunker at the next, however, as he slipped into the lead with Simpson and Edwards.
Edwards was steady throughout. He converted birdies on five and six, then birdied the ninth to climb to 10-under. Edwards birdied the par-4 13th to get to 11-under. He had a good look from 25 feet out at the last, but his birdie putt just lipped out on the low side.
Simpson dropped his approach to nine feet at the par-5 18th. He rolled that putt in for birdie to get to 12-under.
'I've never won on the Champions Tour and to even think about winning at Pebble Beach, you bet I'm nervous,' Simpson said as he waited for the final two groups to finish.
Haas had birdie chances -- from six feet on 16 and 11 feet on 17 -- but missed both. He also had a look at birdie at the last, but his 29-footer came up short and left of the cup, giving Simpson the win.
Simpson and Bill Murray were long-time partners in the Pebble Beach Pro-Am on the PGA TOUR, but have never won the event. Simpson's best personal finish in that event was a share of 15th.
'Obviously to get this win is such a thrill. It's unbelievable,' said Simpson, who collected $300,000 for the win. 'I had so much fun with Bo-bo (his nickname for amateur partner Robert Carter) and I got to play with Bill (Murray) and to have him walk around with us the last few holes was great. Just to win at Pebble Beach, it's hard to sink in.'
D.A. Weibring, Mike McCullough, Loren Roberts and Des Smyth shared seventh place at 8-under-par 208.