Zaniolo, 19, is enjoying a breakout season in Serie A as he continues to impress up front for Eusebio Di Francesco's team.
And he was instrumental in a 2-1 victory over Porto's in Tuesday's first leg, swooping with two goals in six minutes past goalkeeping legend Iker Casillas.
His double meant that Zaniolo became youngest Italian player ever to hit twice in a Champions League tie, a fact that left him elated after the final whistle.
“It’s an incredible night, I am speechless and never would’ve expected such a thing,” he told Sky Sport Italia when questioned on his feat.
Roma will nevertheless take nothing for granted at the halfway stage.
Substitute Adrian Lopez kept the tie on a knife-edge with a late goal for Porto, which means a 1-0 victory would be sufficient in the return match to send the Portuguese team through on away goals.
And Zaniolo admitted that he and his team-mates were annoyed at that slip having worked themselves into a commanding position.
“However, we’ve got the second leg coming up, we shouldn’t have conceded the second goal and we’ve got to think as a unit," he added.
“We allowed Porto practically nothing, so we have to do the same in the second leg to qualify. I worked hard tonight, but I am very happy to do that for this team.
“Celebrating under the curva is an extraordinary feeling, I can’t describe it. I hope to score many more goals under this curva.”
Roma will travel to Oporto for the second leg on March 6 to defend their slender lead.
The Italians are hoping to repeat their exploits of the 2017-18 Champions League, where they won through to the semi finals during a run that included a famous 3-0 win over Barcelona at the Stadio Olimpico.