Tanigawa eagled the par-5 second and eighth holes in a front-nine 30 on Norwood Hills' West Course, the tree-lined layout where Ben Hogan won the 1948 PGA Championship for his second major title.
"I can't tell you the last time I had two eagles on nine holes," Tanigawa said. "The par 5s, I hit them in two and really putts that you really shouldn't make that I ended up holing and making. That was a bit of a bonus."
Barron also eagled the eighth and closed with a birdie for a 68 to match Tanigawa at 8-under 134.
"I hit the shot of my life at eighth, almost made double eagle, and hit a 5-footer for eagle," Barron said. "And then just kind of held on the first few holes of the back nine."
The 53-year-old Tanigawa has two senior titles, the last in 2019 in the major Senior PGA Championship. The 52-year-old Barron also has two Champions victories.