Haas, who was picked to the United States team by captain Hal Sutton, shot a 6-under 66 and is at 8-under-par 136.
Tom Kite, who won the 1992 U.S. Open at Pebble Beach, and Hale Irwin, each posted rounds of 6-under 66 and are tied for third place with D.A. Weibring (71) and Gary McCord (68). That group is knotted at 5-under-par 139.
This is the inaugural year of the event and it is unique on the Champions Tour. The players are paired with two junior players and an amateur. Play was spread over Pebble Beach Golf Links and Bayonet Golf Course over the first two rounds before Pebble Beach takes over on Sunday.
Stadler played at Pebble Beach on Saturday and holed a 15-foot birdie putt at the first. He knocked a 5-iron to 6 feet to set up eagle at the par-5 second, then added an 8-footer for birdie at the third.
At the par-3 fifth, Stadler hit a 7-iron to 6 feet. He rolled in the birdie putt and made it two in a row at the par-5 sixth, when his third landed in a bunker and he blasted out to 5 feet.
Stadler went over the green into a bunker at the famous par-3 seventh and could not save par. He did save par on his final two holes on the front side and earned his spot atop the leaderboard with his play on the back nine.
He hit a 9-iron to 8 feet for birdie at the 10th, then got up and down for par at the 14th. Stadler holed out a wedge from 115 yards for an eagle at the 15th to get to 8 under par.
Haas matched Stadler in the lead at minus-8 with a birdie at No. 18. Stadler went past him with a birdie at the closing hole. He came up short of the green at the par-5 finishing hole, but he hit a lob wedge to 16 feet and converted the birdie putt.
'This game is so much fun when you're making putts,' said Stadler. 'I darn near made everything today. This is my best round here. I'm looking forward to tomorrow.'
Haas collected a pair of birdies on his front side, then drained a 10-foot birdie putt at the 11th. He hit a sandwedge to 6 feet to set up birdie at the 15th and made it two in a row with a 15-footer at No. 16.
Haas landed in a greenside bunker at the 18th with his second shot, but blasted out to 5 feet. He made the birdie putt, then found out some good family news. His son Bill is tied for second at the Deutsche Bank Championship on the PGA Tour.
'Pretty good week for my family,' said Haas. 'When everyone's playing well and making birdies, it makes it fun to go to the next hole.'
David Eger, who held the first-round lead, struggled to a 1-over 73 and is tied for seventh place with Ed Dougherty, who carded a 3-under 69 on Saturday. The pair is knotted at 4-under-par 140.
Lanny Wadkins and Bob Gilder each carded rounds of 3-under 69 and share ninth place with Gary Koch, who shot a second-round, 1-under 71. The trio is tied at minus-3.