Jacobson birdied five of the last seven holes at The Mines as he added a 64 to his opening 65 and reached 13 under par in the PGA Tour-sanctioned event.
But Overton, yet to win on the circuit, had the round of the day - a nine-under 62 with seven birdies and an eagle two on the driveable 15th.
They are one ahead of Bo Van Pelt, who matched Jacobson's round, but there is then a three-stroke gap to three more Americans - Mark Wilson, Stewart Cink and Jimmy Walker - and also Venezuela's Jhonattan Vegas.
Overnight leader Robert Allenby fell six back, meanwhile, when he could manage only a 72, nine more than his first round. It was only one shot off the worst score of the day among the 48-strong field chasing a first prize of 1.3million US dollars (#807,000).
Defending champion Ben Crane is eight back and last year's runner-up Brian Davis is down in joint 40th spot and 13 adrift after another 71.
Jacobson's round actually began with a bogey, but he birdied three of the next five, had four more in a row from the 12th and made a further gain at the long 17th.
Overton, a member of America's Ryder Cup team a year ago, kicked off with three successive birdies, turned in a five-under 30 and came home in 32.
After his course record Overton, a last-minute replacement for David Duval, told the PGA Tour website: "I changed golf clubs a couple of weeks ago and my ball-striking has improved so much."
He flew from Florida to London on Monday, then on to Kuala Lumpur. Arriving Tuesday night he discovered his clubs were not on the plane and for the eve-of-tournament pro-am he used a set belonging to one of his amateur partners.
Jacobson, winner of the Travelers Championship this summer for his first title on the circuit, commented: "The driving has been setting up a lot of opportunities."