Real Madrid earned a 2-0 lead over Valencia in the first leg of their Copa del Rey quarterfinal at the Bernabeu on Tuesday.
The Blancos rode their luck on a number of occasions against in-form Valencia but the victory was a welcome and much-needed boost in light of the champions' poor league campaign, where they already trail leader Barcelona by 18 points.
"It was a tight, physical match in which the goalkeepers kept the score down, although we came close to a third goal," Madrid defender Ricardo Carvalho said.
Both Madrid and Valencia had decent chances to take the lead before Jose Mourinho's players got their noses in front in the 37th minute when Karim Benzema latched onto a pass from Sami Khedira before sliding a low shot past Vicente Guaita.
Valencia forward Jonas spurned a wonderful opening to draw his side level in the 66th minute, and seven minutes later Madrid doubled its lead when Los Che winger Andres Guardado inadvertently turned Fabio Coentrao's cross into his own net under pressure from Gonzalo Higuain.
Cristiano Ronaldo had two great opportunities to increase Madrid's lead late on but on both occasions he was denied by brilliant saves from Guaita.
Mourinho adjusted his midfield by substituting Modric for Angel Di Maria in the 62nd and eight minutes later refreshed his attack by bringing on Higuain for Benzema.
The switch led to Madrid's second goal -- but not without controversy.
Television replays showed Higuain may have just grazed the goal-bound ball with his hand, an action that caused vociferous complaints from Valencia's dugout and led to the dismissal of coach Ernesto Valverde.
"We were clearly hurt by some very poor refereeing decisions," Valverde said.
If Madrid can hold on to its advantage in next week's second leg at the Mestalla then it could meet archrival Barca in the semifinals. Cup holders Barca play the first leg of its quarterfinal against Malaga at the Nou Camp on Wednesday.
Information from Press Association and The Associated Press was used in this report.