Muniain, 27, had been red-carded in his team’s 2-1 defeat to Real Sociedad in La Liga at the weekend.
However, he was the toast of the city Wednesday when he latched onto a cross from Inaki Williams just three minutes before the interval to score the game’s only goal.
Athletic coach Gaizka Garitano named the same team which shocked Barcelona in the quarter-finals last week and they will consider themselves unfortunate not to have won by a greater margin on Wednesday after having two strikes ruled out for offside.
The second, scored off a fine volley in the 61st minute by Ander Capa, needed an intervention by VAR.
“To be honest, we don’t have good feelings after this game. In the dressing room, no one is happy,” said Garitano.
“When you are not happy because you have made mistakes, so be it. But we found it very difficult to create scoring chances.”
Athletic Bilbao won the first Copa del Rey in 1930 with a 3-2 win over Real Madrid.
With 23 titles, they are second on the all-time list to Barcelona who have triumphed 30 times.
However, their most recent success was back in 1984 after a 1-0 win over Barca.
The second leg of the semi-final takes place on March 5.
Thursday sees the first leg of the second semi-final with Real Sociedad taking on second division Mirandes.
