Barcelona have also maintained their flawless start so far after their victory yesterday which takes them top of the table ahead of Madrid on goal difference.
The snub came as a big surprise as the Barcelona great had topped the scorer's charts with 45 goals in all competitions in the 2017/18 season and helped the Catalans win the league and Cup double in Spain.
Any hope of a revival from the visitors was soon killed off by three Barca goals in 11 minutes from Ousmane Dembele, Ivan Rakitic and Messi while Jordi Alba capped a brilliant performance to score and Suarez added goal number eight from the penalty spot in stoppage time. Messi then fired a right-footed shot in off the far post for the 16th-minute equalizer.
Huesca drew closer just before the halftime whistle, with Alejandro Gallar Falguera scoring in the 42nd minute.
Dembele then struck the crossbar with a powerful effort in the 29th minute during a hard period for Huesca.
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Barca's polished second half could not have contrasted more greatly with their sluggish start to the match as they were breached for the first time this term inside three minutes, Hernandez diverting in Samuele Longo's downward header. Cucho Hernandez beat Marc-Andre ter Stegen in the third minute to take the initial lead.
The route was inevitable, with Messi completing his brace on 61 minutes after being sent one-on-one with Werner by Coutinho to finish into the bottom corner.
Barcelona were not to be denied, however, and scored a fourth moments later when Dembele found the bottom corner with an excellent low strike.
Summer arrivals Clement Lenglet, Arturo Vidal and Arthur all entered the field for Barcelona in the period that followed, while Ruben Semedo - in prison earlier this year - entered the field for Huesca.
Messi registered another assist in the 81st minute, sending Alba a crafty through ball toward the far post.