Dowman, who is 15 years and 309 days old, beat German striker Youssoufa Moukoko, who played for Borussia Dortmund at Zenit St Petersburg at 16 years and 18 days in 2020.
Moukoko currently plays for FC Copenhagen, who face Tottenham Hotspur later on Tuesday.
At the post-match press conference in Prague, Arsenal manager Mikel Arteta hailed Dowman's "personality" and "courage".
"He comes in, the first ball he takes, he takes people on, he starts to dribble, he gets a foul," he said.
"You cannot teach that. You have it or you don't, and it doesn't matter what his passport says.
"You throw him in this context and he's there to adapt and have a good performance, so I'm really happy with that," Arteta added.
Dowman made his Premier League debut aged 15 years and 234 days during the Gunners' 5-0 win over Leeds on August 23rd.
He is the second-youngest Premier League player ever after Arsenal teammate Ethan Nwaneri, who was 53 days younger on his 2022 debut.
But Dowman became the youngest-ever player to start a match for Arsenal in the Gunners' 2-0 win over Brighton in the League Cup fourth round last week.