The British number one claimed a confident 6-4 7-5 win against former French Open champion Ostapenko.
Boulter is attempting to win a second grass-court title this month after triumphing in Nottingham.
"It's definitely taken a lot of the pressure off me," Boulter said.
"I wasn't sure what to expect coming into this grass-court season, I'm out here having fun and enjoying myself."
Boulter will be seeded for the first time at Wimbledon this year, meaning she can't face a player ranked in the top 32 until the third round.
But the 27-year-old showed she can compete with the top players, outplaying one of the biggest hitters on the WTA Tour.
"Honestly, I was just trying to slap a little harder than she was," Boulter said.
"She's so tough to play against, you never know what is going to happen and it's completely in her control."
Britain's Emma Raducanu continues her Wimbledon preparations against American second seed Jessica Pegula later on Wednesday.
Earlier, defending champion Madison Keys booked her spot in the quarter-finals with a 7-6 (7-5) 6-1 victory over Ukrainian qualifier Anhelina Kalinina.
Karolina Muchova completed her first full match since September with a 6-4 6-1 win against Poland's Magda Linette.
And in an all-British affair on court two, Billy Harris fought back from a set down to beat lucky loser Charles Broom 3-6 6-2 6-2.
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