Pegula won their previous meeting, a tight three-set match in the Miami Open semi-finals last year.
However, Eala has improved since then, notably on her serve. She won 71% of first-serve points against Osaka, and dropped only four points behind her second.
"I'm more well-rounded [now]. I'm physically a little bit better," Eala said.
"I played really well, had a great mentality and stayed locked in until the end."
Pegula came back from 5-2 down in the first set to beat Russia's Diana Shnaider 7-5 6-4 and reach a second Washington final.
In the men's tournament, third seed Taylor Fritz will face rising Spanish star Rafael Jodar in the final.
World number 10 Fritz hit 13 aces to beat fellow American Brandon Nakashima 6-3 3-6 6-3.
Jodar - who will break into the world's top 20 after starting the year ranked 165th - beat Chile's Alejandro Tabilo 6-7 (6-8) 6-4 6-4.
