Real Madrid pulled away from Leganes in the second half for a 3-0 win in their Copa del Rey first-leg tie on Wednesday.
Despite Madrid dominating possession in the first half, it was Leganes that had the better of the chances, Martin Braithwaite firing just wide of goal on a counter-attack in the 26th minute and then forcing a save from Keylor Navas with a powerful header 10 minutes later.
The hosts had seen two shouts waved off before the referee finally pointed to the spot in the 42nd minute when Gerard Gumbau fouled Alvaro Odriozola in the area and Ramos converted his sixth penalty in all competitions this season.
Madrid again dominated proceedings in the second half and their pressure told in the 68th minute when Cuellar was caught out of his goal and Vinicius Jr. unselfishly laid the ball off for Lucas Vazquez to tap home.
Vinicius would then get his name on the scoresheet in the 77th minute, side-footing home a spectacular, first-time volley from an Odriozola cross to make it 3-0.
Fans stayed away from Santiago Bernabeu on Wednesday after Sunday's shock defeat by Real Sociedad left them 10 points adrift of leaders Barcelona in La Liga.
Solari, who has faced criticism for the team's drab start to 2019, also said the team felt a sense of release after the victory after the Sociedad defeat and last week's 2-2 draw at Villarreal.
"Real Madrid always need to win and always need to score, we came into this game after a match in which we deserved to score but didn't so obviously this result liberates us," Solari added.
"We played very well, we were solid and we deserved this result against a team that was very organised."
The teams will meet again for the second leg at Leganes' home ground on the outskirts of Madrid on Jan. 16.