Dida had already saved shots by midfielder Danilo and defender Edenilson, while Argentine striker Hernan Barcos and Alex Telles failed to convert for Gremio, which is back in the tournament's semifinals for the second consecutive year.
Last year, the four-time Brazilian Cup winner was eliminated by eventual champion Palmeiras in the semifinals. Gremio will now face Atletico Paranaense, which advanced to the semis for the first time by holding Internacional to a 0-0 draw at home after a 1-1 result in the first leg in Rio Grande do Sul.
Internacional was eliminated despite a strong squad containing the likes of Uruguay striker Diego Forlan and Argentine forwards Andres D'Alessandro and Ignacio Scocco.
Another star out of the tournament is veteran Dutch midfielder Clarence Seedorf, whose Botafogo lost 4-0 in a one-sided match in front of more than 50,000 fans at the Maracana Stadium. The teams had drawn 1-1 in the first leg. Striker Hernane scored three goals for Brazil's most popular club, which will play either Vasco da Gama or Goias, which meet Thursday at the Maracana. Goias won the first leg 2-1 at home.
Wednesday's match at the Arena Gremio ended with 10 players on each team. Chilean Eduardo Vargas, who hit the post late in the second half, was red carded along with Corinthians forward Emerson for an altercation near the end.
Brazil World Cup veteran Elano scored one of Gremio's goals in the shootout.
Corinthians played without Peru striker Paolo Guerrero, who is scheduled to undergo right-foot surgery after getting hurt in a league match last week.
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