It was the 26-year-old's top seed, having lifted trophies at Indian Wells and Los Cabos in 2021.
Norrie failed to pick up any of her five break points but won both sets of tough matches in a tie-break with Opelka based at Delray Beach in Florida.
He is the first left hander to win the tournament since 2004.
"I really enjoyed my time on the court at Delray this week," said Norrie after winning in one hour 51 minutes.
"You move great. You play great," he told the world number 20 Opelka. "I'm sure you'll be in the top 10 soon."