Trailing 4-0 from their trip to France in the opening leg of the last-16 clash, Luis Enrique’s men were looking to make history and also avoid their earliest exit from the competition in a decade.
Luis Suarez’s close-range header gave Barcelona the perfect start inside three minutes before an own goal from Layvin Kurzawa halved the deficit by the interval.
A penalty from Lionel Messi five minutes into the second half had the Nou Camp rocking, only for Edinson Cavani to crash in a crucial away goal just after the hour mark which boosted PSG’s advantage.
Neymar, though, netted a superb late free-kick before levelling the tie with a last-minute penalty to get the Barcelona fans dreaming of the impossible once again.
That became a reality when, with goalkeeper Marc-Andre ter Stegen having joined the attack, Neymar lofted the ball into a crowded penalty area.
Roberto stabbed it past Kevin Trapp to spark wild celebrations on the Barcelona bench and in the stands, while PSG watched on in disbelief.