He also scored from the spot as Italy bowed out of the tournament in the semis at the hands of Argentina.
In 1994, despite struggling with injury, he carried the Italian effort almost single-handedly, leading them to the final.
Italy were 1-0 down to Nigeria in the second round and heading out of the tournament before Baggio's late equaliser.
He then won it in extra-time with a penalty.
Another late goal in the quarter-finals saw Italy past Spain and into the final four.
A brace against Bulgaria in the semis handed them a 2-1 victory and Baggio could seemingly do no wrong.
But then came the miss from the spot against Brazil and the final agony which prompted Baggio to say: 'I will always feel a sense of loss.
"It's hard to get so close to something so sacred, knowing you might never get the opportunity again."
He was subsequently dropped by the national side and missed out on Euro 96.
But he did get another chance and was back on the world stage in France for the World Cup in 1998.
He showed flashes of his old self in helping the Italians through the group stages.
He even stepped up to take crucial penalties against Chile in the group stage and France in the quarter-finals - on both occasions he made no mistake from the spot.
But the Italians went out courtesy of the dreaded spot-kicks for the third World Cup in a row and Baggio was unable to exorcise the ghost of '94.
With the likes of Francesco Totti, Christian Vieri, Filippo Inzaghi, Alessandro Del Piero, Vincenzo Montella and Marco Delvecchio to call upon, Trapattoni is hardly short of inspiration up front.
And unfortunately for 'Il Divin Codino', that has spelled the end of his rocky World Cup career.