Federico Valverde also scored in extra time Thursday as Madrid reached the quarterfinals with a 5-2 victory after squandering a 2-0 lead in a 2-2 draw in regulation at the Santiago Bernabeu stadium.
It was the first of a three-game home stretch for Madrid, which on Sunday hosts Las Palmas in the Spanish league and on Wednesday takes on Salzburg in the Champions League.
Budimir netted the winning goal in the 70th to help Osasuna advance two years after it had eliminated Athletic in the semifinals.
Madrid was looking for a comfortable victory to bounce back from the rout against Barcelona. Carlo Ancelotti’s team is trying to keep pace with Atletico Madrid at the top of the Spanish league and improve its standings in the league phase of the Champions League.
Mbappé put Madrid ahead in the 37th minute after picking up the ball before the midfield line and making a run all the way into the Celta area to finish with a left-footed cross shot. It was Mbappé’s second goal in his last five matches with Madrid. Vinícius scored his first goal in five matches after a breakaway in the 48th.
Kylian Mbappé and Vinícius Júnior scored a goal in each half but Celta rallied with goals by Jonathan Bamba in the 83rd minute and Marcos Alonso in stoppage time.
Defending champion ousted
Titleholder Athletic Bilbao rallied from a two-goal deficit in the first half but still lost 3-2 to Osasuna at home.
Real Madrid needed two goals from Endrick in extra time to get past Celta Vigo in the round of 16 of the Copa del Rey and avoid another embarrassing setback less than a week after losing 5-2 to Barcelona in the Spanish Super Cup final.