Ethan Nwaneri and Bukayo Saka scored in the second half at the Emirates Stadium as Premier League leaders Arsenal earned a quarter-final at home to Crystal Palace.
But it was Dowman, still two months shy of his 16th birthday, who stole the show with a dazzling display that climaxed when he was given a standing ovation after coming off in the second half.
Gunners boss Arteta was delighted with Dowman's composed performance, which belied his tender years, even if his shy response to being picked was more in keeping with someone still of school age.
"A tiny smile, that's what you get with him," said Arteta when asked how Dowman reacted when he told him he was starting.
"For him everything is natural, for him everything is OK. It's the way he plays and that's the secret, that he doesn't make a big fuss of it.
"He just does what he does best, which is to play football. To play football with a lot of courage and determination and today again, he has shown some incredible skill, some capacity to run past players at that level in the Premier League at 15. It's definitely something special."
The highly-rated teenager previously came off the bench in the league against Leeds and Liverpool and the last round of the League Cup at Port Vale.
Having got a taste of starting, Arteta expects Dowman to be pushing for more regular action.
"For sure, if you ask him. That's what we have to manage and not only that, there's a lot of things that are new in his life," he said.
"We have to make sure that he takes the right steps and he needs be able to cope with it, too, because it's happening very, very fast and we all need to be aware of that.
"Let's encourage him to keep going that way, but let's protect him as well."