Watson, who will next face Victoria Azarenka, is determined to avoid a repeat of her third-round exits of 2012 and 2015, when she nearly put out Serena Williams.
"She started to step up in the second set but I was able to keep my cool and just stick with her".
The second was a tighter affair but the 25-year-old twice recovered from a break down to run out a 6-0 6-4 victor at the All England Club.
Azarenka is a two-time Australian Open champion but is playing in just her second tournament since giving birth to baby son Leo in December.
She raced through the first set taking it off the Latvian in just nineteen minutes on No.2 Court.
Watson will now face Victoria Azarenka in the third round, and the Brit herself knows that she has to be at her best to prevail in the clash. After these good results, Watson feels very confident about her game, saying, "right now I'm very happy with my game, very happy with how I'm playing, like I've said. I was pleased with how I remained calm and just kept doing what I was doing".
It promises to be a fine contest and Watson will fancy her chances given Azarenka's lack of match practice.
There was a win for eighth seed Dominika Cibulkova on Court 18 who came through 6-4 6-4 against Jennifer Brady of the US.
Watson, who has had a hard 12 months, dropping outside the top 100, made the semi-finals in Eastbourne and is hoping her good form continues.
Kristyna Pliskova was defeated by Maria Sakkari of Greece, ranked 61 places lower than the Czech at 101.
Heather Watson is within touching distance of achieving her long-term goal of reaching the second week of a grand slam - which could be bad news for coach Morgan Phillips. "You don't get to where she's got to in her career without being a really good player".