Tom Watson is alone in second place with 14 points. John Harris,Hugh Baiocchi, Terry Dill and Mike McCullough share third place with 12 points at Park Meadows Country Club.
The modified Stableford format awards eight points for a double eagle, five for an eagle and two for a birdie. No points are given for a par, while one point is deducted for a bogey and three are taken away for a double bogey or worse.
Hatalsky overcame early problems after a pair of bogeys at the fourth and fifth holes. He birdied four holes in a row around the turn, all from inside 20 feet, to collect eight points before a big par save at the 12th.
The par-3 14th is where Hatalsky began to move up the leaderboard. He missed the putting surface from the tee but chipped in from 30 feet to collect two points and move to plus 10.
Hatalsky landed in a bunker off the tee at the par-5 15th but he was able to knock his second shot pin high in the rough, 25 feet from the stick. He chipped in from there for an eagle and five additional points.
'Stableford creates a little variety for us and the fans,' said Hatalsky, a four-time winner on the PGA Tour in the midst of a fine rookie season on the Senior Tour. 'It's fun chipping in for eagles, and you get five points, too. It's like my wife's home cooking. It's good.'
Hatalsky carded a pair of birdies at 16 and 18 to get to 19 points, the most ever in a single round of a Senior Tour event using this scoring system.
'It was a very good day for me,' said Hatalsky, who needed only 21 putts on Friday. 'I missed some short putts early but I shot 30 on the back nine. I was solid, tee to green, and my short game was good.'
Watson recorded five birdies and three bogeys in his round before stepping on the 17th tee. He nailed his drive and knocked a 5-iron to two feet, setting up eagle and making the move to second place.
'I played well despite three bogeys,' said Watson, who was the runner-up in the U.S. Senior Open. 'I'm in a good position. Morris Hatalsky is the man to beat right now. He can putt and really has improved his golf swing.'
A pair of Senior Tour major winners are part of a group with 11 points. Tradition winner Jim Thorpe and U.S. Senior Open champion Don Pooley joined Jim Ahern in a tie for seventh.
Arnold Palmer delighted the gallery Friday when he collected six points in a round that would have been a 71 had it been contested in stroke play.
'Today I had fun,' Palmer said. 'It's been a long time since I played 18 holes and had fun.'
Full-field scores from United Fore Care Classic