An error from Barcelona goalkeeper Neto left Ronald Koeman’s team on a run of four games without a win in La Liga, 12th in the table and eight points behind leaders Real Madrid.
Barcelona and 10-men Deportivo Alaves played a draw with a goal each.
An uncomfortable back pass from Gerard Pique in the first half flummoxed the Brazilian who was robbed by Luis Rioja who scored.
Winger Luis Rioja opened the score in 31st minute to give Deportivo Alaves 1-0 lead.
Jota was sent off in 62nd minute and Alaves remained to 10 men.
Griezmann scored the equaliser in 64th minute to convert Fati’s assist and made it 1-1.
In other LaLiga match, Portugal prodigy Joao Felix scored in either half as Atletico Madrid continued their unbeaten start to the season with a 2-0 win at Osasuna in La Liga on Saturday.
Joao Felix scored twice and Lucas Torreira scored a goal for the victory. Ante Budimir replied a goal.