Tom Watson surged into third place with a total of 26 points after posting an eagle and two birdies over the last four holes at Park Meadows Country Club. Don Pooley, who defeated Watson in a five-hole playoff to win the U.S. Senior Open in June, was fourth with 21.
Jay Sigel and Mike McCullough were next at 19 points while John Bland, Bob Gilder, Jim Ahern and Hugh Baiocchi rounded out the top-10 at 18.
The modified Stableford format, which is being used for the first time in this 21-year-old Senior Tour event, 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 is deducted for a bogey and three are taken away for a double-bogey or worse.
Jacobs exhibited the unpredictable nature of the scoring system, vaulting from a tie for 31st with six points after Friday's action into the lead after seven birdies and two eagles. His second round would have been a course-record 11- under-par 61 had it been contested in stroke play.
As it was, Jacobs' 24 points represented the highest single-day point total in a Senior Tour event featuring modified Stableford scoring.
Hatalsky took the first-round lead with 19 points on Friday, bettering the previous record of 16 set by Bruce Fleisher in the second round of the 2000 Royal Caribbean Classic.
In the PGA Tour's International, the tournament that made the format famous, the one-round record is 20 points, a mark established by Greg Whisman in 1992 and equaled by Tom Purtzer in 1997.
'If I play good, any format is good for me,' said Jacobs.
Jacobs birdied the two of the first four holes, rolling in a 30-foot putt for two points at the 222-yard, par-3 third. He picked up a quick 11 points with three birdies and an eagle on holes six through nine, matching the best birdie-eagle streak on the Senior Tour this season.
Birdie putts from 15 and 35 feet on the 11th and 12 holes, respectively, took him to 19 points on the day. After cooling off with four straight pars, Jacobs heated things up again when he reached the 521-yard, par-5 17th in two with an eight-iron and drained a 10-foot eagle putt.
'I hope I have a big lead at the end,' he said. 'It's going to be a heck of a shootout. The gallery is going to have fun.'
Jacobs, who hit all 18 greens in regulation Saturday, has finished top-10 in this event three of the last four years. His best showing was third in 2000.
'I always seem to have good rounds here, but never seem to get the job done.'
Jacobs captured his fourth Senior Tour title in February at the Royal Caribbean Classic, which returned to its original stroke-play format this year after two seasons as a modified Stableford event. He has seven other top-10 results in 2002, including a runner-up at the season's first major, The Tradition, where he lost in a playoff to Jim Thorpe.
Hatalsky was floundering at the start with four pars and a frustrating bogey at the par-5 fifth. He birdied four of the next nine holes with putts ranging from six to 35 feet, then closed with back-to-back birdies, the last coming on a 25-foot attempt.
'It was a 'blah' kind of day from the standpoint of trying to build any momentum,' said Hatalsky, a four-time winner on the PGA Tour in the midst of a successful rookie season on the Senior Tour. 'Finishing on a good note was good psychologically for me heading into tomorrow.'
Watson hit driver and a five-iron into the par-5 15th green and sank the 12-footer that remained for eagle.
'I had my eye on that putt,' said Watson, who added birdies at 16 and 17 for 12 points on the day. 'I started the ball on the right line and it went right in the middle.
'It's nice to finish strong. It will take another low score tomorrow.'
Steve Veriato, who won this title in stroke play last year, was 61st in the 78-man field with five points for the tournament.
Full-field scores from United Fore Care Classic