Spain stepped up the pressure in the final 15 minutes of regular time, with Villa twice going close. Ramos almost opened the scoring on 77 minutes when he rose to meet a Xavi corner, only to head narrowly over the bar, dpa reported.
Robben was through in the 83rd minuted, but after shrugging off two Spanish defenders he was unable to round Casillas, who smothered the ball.
A minute later the Bayern Munich forward was yellow carded for dissent, after complaining to Webb about the challenges.
Spain substituted Arsenal midfielder Cesc Fabregas for Alonso three minutes before the game went into extra time.