A full court witnessed the 27-year-old overcome Tatjana Maria, the 2022 semifinalist, 7-6 (8-6) 7-5.
Despite being dealt a challenging draw, Boulter overcame a nervous start to defeat the 36-year-old German in just over two hours.
She receives her first seed at SW19 following a successful season that included victories in Nottingham and San Diego.
“I know she made [the] semi-finals here a couple of years ago and I can completely see why,” Boulter added.
She was a fierce competitor who made me work really hard for everything. I think I mentioned that I’m excited for the ice bath.
Zhuoxuan Bai of China was defeated by British number two Dart 6-4 6-0 earlier on Tuesday.
There haven’t been five British women in the Wimbledon second round since 1987, when Emma Raducanu, Lily Miyazaki, and Sonay Kartal all triumphed on Monday.
Boulter stated that she anticipates “an absolute battle” with Dart, her teammate for the Billie Jean Cup.
“Playing a Brit in the UK, on the grass, is never an easy draw,” said Boulter.
Last month, the two played in the Nottingham Open, with Boulter emerging victorious in the opening round match after three sets.
