The 40-year-old's match against Dutch lucky loser Boogaard featured the second-largest age gap in ATP Tour and Grand Slam history. Dominic Thiem was 18 when he beat 44-year-old Thomas Muster in Vienna in 2011.
"I'm happy with the way I was playing," Wawrinka said.
"He's a really young player. He has many years on tour for sure. But I was really happy with the level today. I was focused on myself, trying to be aggressive.
"The conditions are quite slow, so it's never easy really to dictate. But I'm happy with my level so far."
Three-times Grand Slam champion Wawrinka, who said last year that 2026 would be his final season, takes on Australian world number eight Alex de Minaur next.
"He's a tough player," Wawrinka said.
"Especially in these conditions, it's going to be difficult to generate something. But I'm looking forward to the challenge. I've been playing some good matches against top players, so I'm always trying to push myself."
Wawrinka made his Grand Slam breakthrough by winning the 2014 Australian Open and last month became the oldest man to reach the third round of the Melbourne major since Ken Rosewall.
He is expected to play in the other Grand Slams this year before wrapping up his career.