Italian teenager Zaniolo scored both goals as Roma emerged 2-1 winner at home to Porto in the opening leg of their last-16 tie on Tuesday, FourFourTwo reported.
The 19-year-old, who joined Roma as part of Radja Nainggolan's move to Inter in the off-season, became the youngest Italian player with a brace in the Champions League.
Afterward, Zaniolo told Sky Sports Italia, "I have no words, it's a memorable day. I'll never forget it in my life.
"Now I want to focus on the return leg because the goal we gave up can be bothersome. We have to play like we did today without conceding anything to the opponent.
"We had prepared it this way. I ran a lot, but I'm happy for the result. It's a unique emotion to score under the Curva Sud, I can't describe it. I hope to score many more."
Roma was 2-0 ahead in the second half thanks to Zaniolo before substitute Adrian Lopez netted a priceless away goal for Portuguese visitor Porto.
"Obviously, we didn't want to come here and suffer a defeat, but it was a very balanced game," Porto goalkeeper Iker Casillas told TVI. "We conceded that quickly-taken goal, then were unlucky on the second as the ball bounced right back into his path, but this can happen in football.
"I believe we did justice to our performance with that away goal and that means the tie is still open. Although Roma isn’t in the top four in Serie A right now, it does have great players, so we knew it'd be difficult.
"We believe that we can control the second leg and go through."