Pegula, 24, served 10 aces and broke her younger America compatriot five times.
"I've been playing a lot of tournaments lately, so I have been getting a lot of match play, and been doing pretty well, but this is probably the most amount of matches in a row," Pegula told reporters.
Pegula had already beaten Kristyna Pliskova, Ons Jabeur and second seed Petra Martic to reach the semi-final.
After missing seven months with injuries last season, she has enjoyed a much more successful 2018, reaching five semi-finals in ITF events.
"I feel pretty good physically, which has always been the number one thing," Pegula said. "Today, I wasn't that sore or anything.
"I've had some pretty good wins already, so I knew I had the chance to win the match today. I'm excited and I'm just glad I got it done."
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Peter Rutherford)
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