Florenzi raced down the touchline and was just inside the Barcelona half when he spotted Marc-Andre ter Stegen off his line and unleashed a looping effort which flew over the Barca goalkeeper's head and into the net off the far post.
Ter Stegen ran back desperately, then appeared to stop thinking that the ball would go out only to see it land in the goal in the 31st minute of the Group E game.
Luis Suarez had headed Barcelona in front 10 minutes earlier as they began the defence of their title.
"It's not something that happens every day," said Florenzi in a television interview. "Looking at the video now is making me emotional.
"We have climbed Everest," he added. "We were united towards a single goal, to stop this team. We've prepared well, we knew their strengths."
As expected, Barcelona, whose coach Luis Enrique was returning to the club he coached for one season, dominated possession and the Roma crowd was often strangely silent as the visitors stroked the ball around in midfield.
But Roma had clearly learned the lessons from the 7-1 home defeat to Bayern Munich just under way year ago and managed to keep the visitors down to a handful of scoring chances.
"I was very pleased with our defensive organisation," said Roma coach Rudi Garcia. "Tactically, we were almost perfect."
Lionel Messi, making his 100th Champions League appearance, and Suarez both had early chances before Barcelona prised open the Roma defence in the 21st minute.
Jeremy Mathieu floated a long ball over the defence which set Ivan Rakitic clear on the right and the Croat's cross was headed in by Suarez at point-blank range.
Barcelona were threatening to over-run the hosts when Roma right-back Florenzi brought the house down with his spectacular effort.
Barcelona also had the better of the second half although, with Neymar failing to spark, they created few real chances until Messi hit the bar with 12 minutes left.
Barcelona almost won it in stoppage time but Jordi Alba's flicked effort was cleared off the line by a Roma defender.
"We played a complete game and we deserved a better result. We had the game under control," said Luis Enrique.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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