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The 19-year-old, making his debut in the knockout phase of the competition, stuck twice in the second half to give the Giallorossi the advantage in the tie - although an away goal from Adrian Lopez with just over 10 minutes remaining means the place in the quarter-finals is very much still in the balance.
But Eusebio Di Francesco's side were fully deserving of their victory - with Edin Dzeko twice hitting the post during the game and veteran goalkeeper Iker Casillas forced into a number of other important saves.
In truth it was a last-16 tie that took some time to spark into life - with the first half seeing the fewest shots on goal in the competition so far this season. One of them, however, was incredibly close - as Dzeko saw his beautiful turn and shot rewarded with the agony of seeing the drive ricochet away off the near post.
In the second half the Giallorossi continued to turn the screw - but it wasn't until the 70th minute that the deadlock would finally be broken. Dzeko, provider this time, found Zaniolo inside the box - and the youngster made no mistake as he drove a low shot across Casillas and into the far corner.
Soon after the same duo would combine again: this time as Dzeko's low shot cannoned back out off the post - leaving Zaniolo in the right place to sweep home the rebound.
The Olimpico was ecstatic at this point - only to see their mood dampened almost immediately as Adrian escaped inside the box to grab Porto a vital away goal.
And that was how the game finished, meaning the Giallorossi still have a lot of work to do in March's second leg encounter.
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