Konta is competing in her hometown tournament and will be hoping to replicate her semi-final runs of 2016 and 2017.
The contest lasted just an hour and 14 minutes and Konta hit a total of 16 winners, with Yastremska misfiring 33 unforced errors.
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"I'm pleased - I knew Dayana was a big hitter," Konta said.
"There was always going to be very little in it, regardless of the score and the second set could have gone either way."
Elsewhere in British interest, Katie Swan was defeated in three sets by Zhang Shuai and Harriet Dart let a one-set lead slip against Anett Kontaveit.
Maria Sakkari breezed past Jessica Pegula with the loss of just three games and Elise Mertens defeated Olympic champion Monica Puig.
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