Lionel Messi scored the first goal, evading numerous challenges on the right wing and then surged into the area before firing home a firm, low shot.
Neymar tapped in his 38th goal this campaign, before Messi scored his 58th with the outside of his boot.
Inaki Williams for Bilbao headed in late on.
That effort in the 79th minute was a small blip in an otherwise superb performance by Luis Enrique’s side at their home, the Nou Camp.
In France, Ligue One winner, PSG also won the 2015 Coupe de France 1-0, completing the first domestic quadruple in French footballing history. Thanks to a lone strike from Edinson Cavani, who made PSG got the better of Auxerre’s resolute defence.
In Germany, Wolfsburg lifted the 2015 DFB Cup thanks to a 3-1 win over Borussia Dortmund in Berlin’s Olympiastadion.
Pierre-Emerick Aubameyang gave Dortmund a dream start, but Luiz Gustavo brought the Wolves back on terms before Kevin De Bruyne put Dieter Hecking’s men in front. Bas Dost added a third before half-time, wrapping up victory for the Wolves and inflicting defeat on Jürgen Klopp in his final game as Dortmund coach.
*Source: BBC Sport