It was Vinicius Junior who scored for Madrid, which beat Valladolid 3-0 in the previous round but had opened its title defense with a 1-1 draw at Mallorca.
Kylian Mbappé remained scoreless and defending champion Real Madrid settled for a 1-1 draw at Las Palmas in the Spanish league.
Mbappé, Madrid's biggest signing in years, is yet to score in the league this season. His only goal with Madrid came in the team's UEFA Super Cup victory against Atalanta earlier this month.
It was Vinicius Junior who scored for Madrid, which beat Valladolid 3-0 in the previous round but had opened its title defense with a 1-1 draw at Mallorca.
"It's been difficult for us to be as solid as we were last season," Madrid coach Carlo Ancelotti said.
"We need to find a solution quickly, and I think we are going to find it. It has been harder than expected. These first three matches showed me a lot of things that have not been working well."
Vinicius found the net for his first league goal this season by converting a 69th-minute penalty kick after a handball inside the area.
The hosts had taken the lead five minutes into the match after Alberto Moleiro got past a couple of defenders before finding the net from inside the area.
Young Br azil forward Endrick, who scored against Valladolid in his debut, came off the bench in the 86th to replace Vinicius Junior.
Las Palmas is yet to win this season, having drawn against Sevilla and lost at Leganes.
Barcelona on Tuesday became the only team with three wins in the first three rounds after a 2-1 victory at Rayo Vallecano.
Girona, the surprise team last season after a third-place finish, earned its first win with a 4-0 rout of Osasuna at home.
Bryan Gil scored in the first half, then Viktor Tsygankov, Abel Ruiz and Cristhian Stuani sealed the victory in the second.
Girona had opened with a draw and a loss. Osasuna had a draw and a win from its first two matches.