Real Madrid's Cristiano Ronaldo from Portugal, center, vies the ball with Valencia's Victor Ruiz, left, and Ricardo Costa from Portugal, right, during their a Copa del Rey soccer match at the Mestalla stadium in Valencia (photo: AP)
Karim Benzema netted just before halftime to put Jose Mourinho's side 3-0 up in the tie, before Coentrao picked up a second yellow card for a handball in the 51st minute.
Valencia pulled a goal back from the ensuing freekick when Tino Costa's low freekick surprised Real's reserve keeper Antonio Adan.
Adan had to replace Casillas in the 15th minute after Alvaro Arbeloa accidentally kicked his hand while trying to clear a ball.
The injury to Spain's number one did not appear to be too serious as he was later seen in the dugout with ice on his hand.
Di Maria picked up a foolish red card two minutes from time after kicking out at Valencia defender Joao Pereira as the two tussled for a ball.
Real will face either holders Barcelona or Malaga in the last four. Barca visit the Rosaleda on Thursday with their tie level at 2-2.
On the other side of the draw, Alvaro Negredo scored twice to help Sevilla past nine-man Real Zaragoza with a 4-0 quarter-final second leg victory.
The Spain striker netted with a header and a penalty, while Ivan Rakitic and Manu del Moral grabbed the others to complete a 4-0 aggregate win.
Zaragoza had defender Jose Fernandez sent off with a straight red card after only 26 minutes, and midfielder Fran Gonzalez followed him down the tunnel in the 66th, after giving away the penalty for Sevilla's third.
The 2010 Cup winners will meet either Atletico Madrid or city rivals Real Betis in the last four.
Atletico, who lost against Sevilla in the final three years ago, hold a 2-0 advantage ahead of Thursday's trip to play Betis.
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