The 18-year-old, who was on target in a 3-0 victory over Qarabag, has become the second youngest player to score for the Gunners and the first born in the 21st century to net for the club.
The highly-rated midfielder, who is a product of a famed academy system in north London, hopes his continental efforts are just the start of bigger and better things to come.
He turned down the chance to leave Emirates Stadium in search of more regular game time during the summer, with there a desire on his part to prove himself under Unai Emery.
Smith Rowe, who has also seen Carabao Cup action this season, told reporters on his decision to stay put: “It was a chance I took [not to leave] and I am happy I have taken it because now he [Emery] is really happy with me, he helps me a lot and to get the chances I am getting now is crazy.
“I think he is a great manager. There’s no other place I’d rather be.
“I haven’t really set targets. For me, it is just training every day, working hard and, if I get my chance in the Premier League one day, that would be unbelievable. At the moment, I am just trying to make my way with games in the cups. Hopefully, one day, I can make my Premier League debut.”
While chasing down further senior recognition with Arsenal, Smith Rowe is also hoping to follow in the footsteps of fellow teenagers Jadon Sancho and Mason Mount, who have just made Gareth Southgate’s England squad.
“It is a great achievement for those two,” said a talent who has already represented his country up to U18 level.
“It is definitely something I am trying to do in the future and England is a great way to express your ability. They definitely try to give youngsters a chance.
“The England youngsters are a very talented bunch and I think in the future there will be a lot of them going through to the first team.
"Hopefully, one day, I can be part of the team. [Emery] told me to get into the box more and in training I am trying to work on my finishing, working hard.
“[Frank] Lampard scored a lot of goals, so I’m watching his clips, I like watching clips of a lot of players. So, when I am just chilling at home, I watch clips of players.”