Atletico Madrid took advantage of Barca's stumble as Antoine Griezmann's winner against his former club two minutes from time earned a hard-fought 2-1 win over Real Sociedad to move to within six points of the leaders.
Real Madrid's recent La Liga struggles continued on Saturday night with a 0-0 draw against Athletic Bilbao.
Messi then took control of the game as Barca pressed and finally broke Celta's resistence just after the hour when his pass freed Jordi Alba to tee up Suarez for his first goal at the Camp Nou in nearly three months.
Until Saturday, he was in the leading group but with the same number like Pablo Alfaro, retired Spanish player of Sevilla and Aguado, retired Spanish defender of Real Zaragorza, to 18 red cards.
Zidane, though, rejected widespread suggestions, most recently from Valencia coach Marcelino Garcia Toral, that Madrid's squad is poorer this season for the loss of Alvaro Morata, James Rodriguez and Pepe in the off-season.
"We'll keep working at it and I'm sure we'll be there or thereabouts at the end".
Once Zidane's side return to Spain, they will head into the winter break on the back of a first Clasico clash of the season with Barcelona on December 23. Defending champions Madrid are already through to the last-16 along with Tottenham.
"He is so good that when things don't go as he is used to then people start to talk about him", Zidane said on Tuesday ahead of Real's Champions League dead rubber against Borussia Dortmund. Ronaldo and Benzema again missed chances to find the net, which has become a worrying recurring theme for the European champions this season.
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