Wednesday's 2-1 King's Cup quarter-final first-leg defeat by Barca and the controversy surrounding Pepe's alleged stamp on Lionel Messi's hand had left Jose Mourinho's side reeling, with local media reporting a rift in the dressing room.
Barca trimmed Real's lead to two points earlier in the day when Lionel Messi's hat-trick helped the champions to a 4-1 win at Malaga but Real responded with a gritty performance against dangerous opponents to give themselves a lift ahead of Wednesday's Cup return leg at the Nou Camp.
"We knew it was going to be a very, very tough game but we managed to play the ball around well and it was an extremely important win for us," Marcelo, who netted Sunday's equaliser, told Spanish television.
Asked about the reported rift between Mourinho and some of Real's Spanish internationals, the Brazilian added: "If there was any division you would have seen it on the pitch. We showed tonight that there is no problem."
Bilbao's brave challenge fizzled out as their players tired and substitute Jose Callejon added an 86th-minute fourth before Gonzalo Higuain struck a shot against the post.
Barca's earlier game at Malaga's Rosaleda stadium had a distinct Qatari flavour.
The Andalusian club were bought by a member of the nation's royal family at the end of the 2009/10 season and the Barca players shirts are emblazoned with the name of their sponsors, the Qatar Foundation.
World Player of the Year Messi leaped to nod Adriano's floated cross into the bottom corner in the 33rd minute before Alexis Sanchez made it 2-0 three minutes into the second half.
