It was Barcelona’s first ever win against Liverpool at the Nou Camp in a European competition (previous four meetings saw Barcelona lose two and draw two).
Liverpool were dealt an early injury blow in the 24th minute as Naby Keita was replaced by Jordan Henderson.
Barcelona went 1-0 up in the 27th minute thanks to Suarez who ghost past his markers and poked in Jordi Alba’s low cross.
Liverpool had their first big chance in the 35th minute but Sadio Mane could not bring his effort from a well timed cross from Jordan Henderson.
James Milner almost equalised for Liverpool one minute into the second half only to see his curled shot tipped away for a corner by Marc Andre Ter Stegen.
Ter Stegen was called into action again in the 53rd minute as he tipped away Mohamed Salah’s low drive for a corner.
Liverpool continued to create chances and almost got rewarded in the 59th minute but Milner shot straight at Ter Stegen after a brilliant dummy by Georgino Wijnaldum from Salah’s cross.
Barcelona could have scored a second goal in the 64th minute after Messi found an unmarked Arturo Vidal but the Chilean’ s low cross was cleared away by Virgil van Dijk.
With 15 minutes remaining Messi made it 2-0 as he tapped into an empty net after Suarez’s initial effort came off the bar.
Messi grabbed his second and Barcelona’s third goal on 82 minutes with a superb free-kick into the top corner.
Liverpool almost responded immediately but Salah’s effort hit the post after Roberto Firmino’s goal bound shot was blocked on the line.
Barcelona had a golden chance to score a fourth off a counter but Ousmane Dembele hit his effort straight at Alisson.