Barcelona stumbled again, and Real Madrid wasn't able to capitalize.
Griezmann almost found the equaliser after the interval, but the offside flag was raised as he headed the ball into the net.
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. "I know what he has but not how long it will take him to recover".
"The most important thing is victory and it will give us confidence - now we are going to try to win [against Chelsea] because we have the team to do it".
Madrid also lost ground to third-place Atletico Madrid, which defeated Real Sociedad 2-1 at home with a late winner by Antoine Griezmann.
The result could see second-placed Valencia move to within two points of the leaders if they beat Getafe on Sunday.
It was the first time Zidane fielded the same 11 Madrid used when it defeated Juventus in the Champions League final this year. "They have a great offensive play, good aerial play in the boxes and work really well when they attack".
Celta's lead lasted two minutes, though, as Messi latched onto Paulinho's pass to fire low under Ruben Blanco for his first goal since late October.
Later on Saturday, Real Madrid missed a chance to move closer to Barcelona after being held by Athletic Bilbao to a goalless draw as Sergio Ramos set an unwanted La Liga record.
"There is still a lot of league left", Atletico coach Diego Simeone said.
However, Griezmann's bravery was rewarded with a fourth goal in three games when he slid in to meet Saul's looping header despite being sandwiched between a Sociedad defender and the far post.
In the 70th minute, Atletico fans were finally put out of their misery as Simeone signalled for a double substituion which saw fan favourite Fernando Torres come on for Kevin Gamierio but more importantly saw Angel Correa go off for Carrasco.
"I waited, I waited, and I kept waiting [for Arsenal]".
- Atletico Madrid has equalled its longest ever unbeaten run in LaLiga (W11 D7), recorded twice previously (18 in 1991 and 1941).
Brazilian ace Jose stepped up and buried the strike confidently down the middle from the spot. When they are on the field, the team keeps on improving, especially in our offensive play.
Atleti looked to continue applying pressure as they came out for the second half and created numerous chances early into the period.
Sevilla moved to within eight points of Barcelona by defeating Deportivo La Coruna 2-0.