In an engrossing, even battle at Petershill Park in Glasgow, Alessandro Spugna's side squandered chances at one end yet simultaneously rode their luck at the other at times - before ultimately earning the victory they probably deserved through the lottery of spot-kicks.
With Camelia Ceasar making the only save of the first nine attempts, the responsibility fell to Emilie Haavi to secure victory - and the Norwegian duly did so with a nevertheless finish.
"It's a night we won't forget," club captain Elisa Bartoli said.
"We put in a great performance ... we deserved to win and we managed to do just that."
The Giallorosse will now wait to find out their opponent in the next phase of the competition, a two-legged head-to-head clash against another winner from the League Path.
The winner of that tie will reach the group stage.
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After beating Glasgow City 3-1 on Thursday night to reach this stage, Roma knew they would be forced to step up their game against an opponent of the quality of Paris - who finished third in the star-studded French league last season.
After an aggressive start from both sides the game settled into a rhythm, with neither midfield offering much in the way of glaring openings for the other side to expose.
Chances were at a premium; althought Benedetta Glionna did hit the bar with a rifled free-kick and both Giada Greggi and Andressa Alves went close at either end of the 90 minutes.
With nothing to separate the sides at that point - thanks also to some solid defensive work from Ceasar and her teammates - the game went to extra-time. Once again, both sides created chances - but once again putting the ball in the back of the net proved frustratingly elusive.
That meant penalties would have to decide the contest. The crucial moment came early on, as Ceasar denied France international Clara Mateo to enable the Giallorosse to take an early lead.
With Manuela Giugliano, Andressa Alves, Annamaria Serturini and Elena Linari all scoring, that paved the way for Haavi to have the opportunity to decide the game - a chance she duly took.
"It's a dream - in the fifth year we have been able to do something that we've been dreaming about for a while, thanks to hard work and the sacrifices we've made," Bartoli added.
"We will enjoy this moment and soon we'll see everyone back in the most beautiful city in the world."
See all the best photos from the game in our gallery below!
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