On a roasting Court Two, the Briton was in the hottest of form in the first set, bashing big forehand winners past her Latvian opponent to clinch it in less than 20 minutes.
Although Sevastova stabilised in the second set, twice going a break ahead, she was unable to arrest the Briton's momentum as Watson became the first player -- man or woman -- to reach the last 32.
"Starts are very important, but I'm really happy with the second set because she raised her level," smiled Watson.
"The first set I just felt great, pretty flawless. It's always going to change. I've got to expect her to raise her level and to try something new, and she did. I was pleased with how I remained calm and just kept doing what I was doing."
Watson will next face Victoria Azarenka after the Belarussian, back on tour after giving birth to her first child in December, ousted 15th-seeded Russian Elena Vesnina.
"I look forward to playing her," Watson said. "I know she has only just come back, but I expect her to be playing really well because I know she will have put in the hours and the work.
"You don't get to where she's got to in her career without, you know, being a really good player."
(editing by John Stonestreet)
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