The Argentine skipped superbly past four players in a mazy run after 20 minutes before shooting venemously into the bottom corner of the net beyond keeper Iago Herrerin to claim his 33rd goal in his 50th appearance for Barca in the competition.
Messi has been in top form in the second half of the season and again provided the inspiration for his team who went 2-0 up when Brazilian Neymar slotted the ball into an open goal having been set up by Uruguay's Luis Suarez in the 36th minute.
With the Bilbao defence dozing, Messi nipped in to clip home a Dani Alves cross after 74 minutes.
A flicked Inaki Williams header gave the Basque side a consolation strike with 10 minutes to go before tempers frayed following some showmanship and play-acting from Neymar.
Barca's South American attacking trio have netted a Spanish record 120 goals in all competitions this season, two more than Cristiano Ronaldo, Karim Benzema and Gonzalo Higuain managed in 2011-12 for Real Madrid.
It was also a record-extending 27th King's Cup title for the Catalans who have also won La Liga this season and will meet Juventus in the Champions League final in Berlin next Saturday.
"They pressed us at the beginning but after that we were the better side," Neymar told reporters.
The Brazilian had a goal harshly ruled offside and Suarez had a shot saved by Herrerin as Barca took an early grip on the game.
Messi then provided a moment of genius to unlock the Bilbao
defence.
The dazzling forward went round three players out on the wing before evading Aymeric Laporte inside the area and finishing clinically with his left foot.
"Leo is incredible...for me the best in the world," said Neymar. "It is an honour to be part of this team with players that have so much ability."
Barca began to find more openings and a well-worked move saw Ivan Rakitic find Suarez in the area and he rolled the ball square for Neymar to score with ease.
Luis Enrique's team concentrated on keeping possession in the second half as Bilbao flagged.
Messi took advantage with his second goal before Williams headed in for Bilbao.
(Editing by Iain Rogers)
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