Lionel Messi missed a penalty but still scored twice, including an exquisite free-kick, as Barcelona edged a five-goal thriller with Valencia on Sunday to stay within touching distance of the top of La Liga.
After Real Madrid and Atletico Madrid both won on Saturday, there was no margin for error at Mestalla, where Barca's 3-2 win reduced the gap behind Atletico back to two points, now with four games left to play.
Gabriel Paulista headed Valencia in front early in the second half before Messi missed a penalty, only to smash in from the resulting scramble.
Griezmann and a superb Messi free-kick looked to have then made the victory secure but Carlos Soler's stunning strike from distance left Barcelona holding on at the end, a nerve-wracking win meaning they could overtake Atletico Madrid next weekend if they beat Diego Simeone's side at Camp Nou.
"We knew we would not have any calm games," said Gerard Pique. "We are still in the fight. Calm games mean you're not competing for anything."
After a frantic week in which Real Madrid drew against Real Betis, Atletico lost to Athletic Bilbao and Barca were beaten on Thursday by Granada, order has been restored to some extent this weekend, with all the top three back to winning ways.
Sevilla are now six points behind Atletico and will need to beat Athletic Bilbao on Monday to stay in the mix ahead of their own crunch game next weekend away at Real Madrid.
"The only idea against Atletico is to win," said Pique. "I hope we will be top by the end of the weekend but even if someone else is there, I wouldn't put my house on them being champions."