World number three Pegula, who won her first WTA title in 2019 at Washington, fell behind 5-2 at the start but battled back to reach her fourth final of the year.
"It was playing a little bit slow. She's a lefty. It's tricky," said Pegula. "I just kept telling myself it's just one break. Just keep holding.
"I found a little rhythm on the return, served a little bit smarter and I was able to play some good tennis, kind of take control of the momentum."
Shnaider grabbed a 5-2 lead at the start but Pegula charged back to capture the next five games and take the first set in 45 minutes.
The Russian served for the set in the eighth game but Pegula broke, held at love, then broke again and held for the set when Shnaider sent a forehand wide.
In the second set, Pegula broke for a 3-2 lead when Shnaider netted a backhand and took a 5-2 edge with a break on a forehand winner.
Shnaider broke in the eighth game but Pegula served for the match again in the 10th game and smashed a forehand winner to advance after 87 minutes with her WTA-best 38th match triumph of the year.
Pegula, a semi-finalist at this year's Australian Open, seeks her 12th career WTA title after hoisting trophies at Dubai and Charleston this season.
