The 21-year-old Filipino left-hander delivered an impressive victory over the four-time Grand Slam winner from Japan to reach her second career WTA final, having dropped the first last year at Eastbourne.
Giant killer Eala, ranked 28th, had previously ousted second seed Elina Svitolina for her sixth top-10 victory of the year after dethroning 2025 Washington champion Leylah Fernandez.
Osaka, ranked 13th, was thwarted in her bid for an eighth career WTA title and first since taking the 2021 Australian Open.
In the first set, Eala took a 2-1 lead by breaking when Osaka sent a backhand wide, but Osaka broke back in the fourth game when Eala netted a forehand volley.
Osaka saved three break points in the ninth game but followed with two errant forehands to surrender a break, and Eala held at love on a service winner to capture the set in 38 minutes.
Osaka double-faulted away a break to begin the second set and netted a backhand to surrender another break and hand Eala a 5-2 edge.
Eala, who reached the fourth round last month at Wimbledon, then held serve to end matters after 76 minutes.
Pegula, seeking her 12th career WTA title and third of the year, eliminated Russia's Diana Shnaider 7-5, 6-4 in the other semi-final.
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