Ostapenko beats Putintseva to reach Wimbledon last eight
Tha 27-year-old Latvian, whose only Grand Slam title came at the French Open in 2017, broke her Kazakh opponent five times in the match, hitting 29 winners against 26 unforced errors.
"This is one of my my favourites on the tour," said Ostapenko. "I won it at juniors (in 2014) and I have great memories here.
"I feel like I'm playing really good players but I'm good in deciding moments. I think that's the key and I'm doing pretty OK."
The 13th seed, a semi-finalist at Wimbledon in 2018, next faces either US 11th seed Danielle Collins or Barbora Krejcikova of the Czech Republic.
Russian-born Putintseva, ranked 35, beat world number one Swiatek in the last 32 on Saturday.