The Gunners went into the clash 1-0 down on aggregate following defeat in Portugal, and were hoping to avoid an eighth consecutive elimination from the Champions League at the last 16 stage.
Any fears were marginally dispelled by Leandro Trossard's precise first half strike following a magnificent pass from Martin Odegaard.
But they couldn't find the goal that would take them through on aggregate in what was a hugely physical contest by full time.
The game went to extra time and penalties - the first time that had happened in a non-Champions League final knockout stage clash for eight years.
But regardless of the outcome in the shootout, Arsenal had already broken a club record.
They had gone three Champions League games without conceding a goal at home, winning all three by an aggregate score of 12-0.
By winning against Porto, they made it four consecutive games this season without conceding - therefore breaking a club record in the process.
And the night got even better for the Gunners as they prevailed on penalties, with Wendell's penalty crashing off the post before David Raya pulled off a magnificent save low to his right to keep out first leg goalscorer Galeno.
Arsenal stars, meanwhile, remained calm from the spot, with Martin Odegaard, Kai Havertz, Bukayo Saka and Declan Rice all finding the back of the net.
It wasn't a straightforward night for Arteta or his players - Champions League knockout matches rarely are - but with an international break on the horizon, the Gunners now know they will be preparing for a dual assault on the Premier League and Champions League once club football gets back underway at the end of the month.
