Watson combined some excellent movement on the grass with some heavy hitting and outclassed her Latvian opponent to reach the third round for a third time.
She teamed up with coaches Phillips and Colin Beecher in the spring at the start of the clay court season and it appears to have achieved the right results after reaching the semi-finals in the Aegon International Championship at Eastbourne last week.
"Whoever I play in the third round is a very tough match, and I have no idea what the draw is".
'I'm winning so it's hard not to be happy but it's about balancing the highs and lows, not making them more dramatic, to be more level-headed'.
French Open champion Jelena Ostapenko fought back despite a string of errors to beat Canadian qualifier Francoise Abanda 4-6 7-6 (4) 6-3 and reach the third round at Wimbledon for the first time.
"I felt very good at the beginning of match, very on it and relaxed, more than I was in my first match", she told the BBC.
She will face either No.15 seed Elena Vesnina or former world number one Victoria Azarenka in round three. Against such an aggressive player like Sevastova, Watson credited her win to some tactics, "Uhm, I just kind of went out just focusing on myself, not too much on what she was going to do".
"I was pleased with how I remained calm and just kept doing what I was doing". It's always going to change.
3 was in splendid form as she downed the 18th seed 6-0 6-4, playing some of the best tennis she'd produced for a number of years. "I obviously know how she plays, she is a great player and was expecting and was prepared for the best. You don't get to where she's got to in her career without, you know, being a really good player". I've got to expect her to raise her level and to try something new, and she did.