The 57-year-old Austin had three straight birdies on Nos. 13-15. He has four senior victories after also winning four PGA Tour titles.
Austin took a 10-under 134 total into the final round at Snoqualmie Ridge.
“It will be fun,” Austin said. “I mean, that’s all you ever ask for is a shot and I give myself a shot and I’ll see how it goes. … I’m always confident. I think I can beat anybody on any given day.”
Furyk and Montgomerie, playing in the same group, each shot 67.
The 51-year-old Furyk won in his first two senior starts last year and took the U.S. Senior Open last month in Nebraska.
The 58-year-old Montgomerie birdied the final two holes. He won the last of his seven senior titles in 2019.
“I enjoyed playing with Jim Furyk, I must admit,” Montgomerie said. “A gentleman and someone I’ve admired for many, many years since we first came across Jim in ’97 at Valderrama at the Ryder Cup. I’ve always admired his game and it’s great to play with him here in America.”
Brandt Jobe, the 2019 winner in the event that was canceled last year because of the COVID-10 pandemic, was 1 over after a 75.
Two-time Boeing winner Bernhard Langer was 6 under after a 68.
Local favorite Fred Couples shot a 69 to get to 3 under.
“It was a little better,” Couples said. “I hit a few good shots and I made a few putts.”