There were 30 groups left on the Caves Valley Golf Club course when a storm moved in late in the day, eventually forcing play to halted.
The sensational round by Eaks included a 15-foot eagle putt and moved him into the tournament record book for lowest 18-hole score alongside Orville Moody (1989), Bruce Fleisher (2000) and Jay Sigel (2001).
"I'm having a blast," said Eaks, who had eight birdies and three bogeys to go along with his eagle. "I've been waiting three years for this. After I made that eagle, I thought I could get something going."
If he could hold on, Eaks would become the youngest player to win the Senior Open. Eaks turned 50 on May 22 and would surpras 1986 winner Dale Douglass, who was three months, 24 days past his 50th birthday.
Wastson, hoping to win the Senior Open 20 years years after winning the U.S. Open at Pebble Beach, was alone in second at 67 while James Mason and Jose Maria Canizares both shot a 3-under 68. Tom Kite and and Allen Doyle were also at 3-under with two holes to play when the rains came.
Only 13 players were under par on a course hosting the tournament for the first time.
Eaks began play on the back nine and birdied three straight holes starting at the 11th. He made the turn in 4-under, then birdied the second and eagled the third.
He admitted thoughts of a 59 entered his mind, but he bogeyed both the fifth and seventh holes to erase those hopes.
Mason is trying to add an Open title to what has already been a career-making year. After driving around the country taking part in Senior Tour Monday qualifiers, Mason won the NFL Golf Classic earlier this month. Mason had committed to playing about 30 Monday qualifiers this year.
Mason had six birdies and a near hole-in-one, but did suffer a double bogey at the par-4 sixth.