Suarez easily tapped home the opener and then Messi finished off a sublime move, before Suarez volleyed in his second.
Gerard Pique made it 4-0 from close range and Messi rounded it off with another.
Adriano smashed in after Neymar had his penalty saved before Edin Dzeko headed in the consolation in stoppage time.
Former Manchester City forward Dzeko also headed over from close range and had a penalty saved by Marc-Andre ter Stegen.
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