Vaughan, who took up golf in his spare time while working as a fireman in Kansas, shot an even-par 71 over the Royal Troon course for a two-day total of 3-under 139. He was a shot in front of John Cook and two ahead of Bernhard Langer, first-round co-leader Eduardo Romero and three-time champion Tom Watson.
"I'm not at all nervous," said Vaughan, who has the 36-hole lead of a senior event for the first time.
Vaughan shared the opening-day lead with Romero despite suffering a double bogey and triple bogey.
Greg Norman, who at age 53 came close to becoming the oldest major championship winner ever last week at the British Open, survived the 36-hole cut by shooting a 72. He had a 36-hole total of 147.
Norman, whose British Open showing qualified him for next year's Masters, said he was close to making a decision about whether he would accept an invitation to next month's PGA Championship.
"I've almost made up my mind," he said. "But I won't make a decision until late Monday night."