The 52-year-old Peoples matched his career best with a 10-under 62 on Saturday to take a three-stroke lead in the Champions Tour event.
"It was pretty much a dream round out of nowhere," Peoples said.
Peoples, who twice shot 62 on the PGA TOUR, made six straight birdies at the TPC Twin Cities to get to 10 under through seven holes, also birdied Nos. 10, 12 and 13 and closed with an 8-foot birdie putt on No. 18.
Winless on the 50-and-over tour, he had a 14-under 130 total.
The last time Peoples led going into the final round was the 1990 Buick Southern Open. Peoples has played 303 PGA TOUR events and 50 Champions Tour events since his last win at the 1992 Anheuser Busch Classic.
He knows he'll be "a nervous wreck" on Sunday.
"You just got to hit the first tee shot, progress through the round and take each shot as they come," he said. "We'll just see what happens."
In nine previous starts this year, Peoples has finished better than 50th only twice. The two-time PGA TOUR winner was third in the Minnesota event two years ago for his best Champions Tour finish.
"I was doing a lot of things wrong in my golf swing and it became a habit," Peoples said. "One thing kind of compounds itself and leads to another and you start compensating for the way you're swinging."
That changed about six weeks ago when he got more body rotation into his swing, rather than leaning and lunging at the ball.
The 58-year-old Romero went back to a belly putter last week in the Senior British Open.
"Now I have a lot of confidence on my putt," he said.
His 1.607 putting average this week is seventh best in the field.
"My game from the tee to the green is fantastic, and then on the green it wasn't, but no more," he said.
Olin Browne (67) and Joel Edwards (69) were 9 under, and Lance Ten Brock (65), Tom Kite (67), Bernhard Langer (69), Mark McNulty (70), Chien Soon Lu (71), Steve Pate (71) and Peter Senior (71) followed at 8 under.
Defending champion Jay Haas was 12 strokes back after his second straight 71.
The course received an inch of rain overnight, further softening the greens. Fifty of 81 players broke par Saturday, one more than were in red numbers Friday.