On their first LaLiga trip to Camp Nou, the newly promoted minnows briefly continued what has been a dream start to the season by sensationally opening the scoring through Juan Camilo Hernandez.
But it proved little more than fleeting joy as Messi, Suarez and a Jorge Pulido own goal swiftly erased the early concern.
Alex Gallar did give Huesca a second reason to celebrate late in the first half before the gulf in class become evident over a one-sided second period.
Messi and Suarez completed their braces at either end of the half and Ousmane Dembele, Ivan Rakitic and Jordi Alba all joined in the fun as the hosts comprehensively maintained their perfect start to the campaign.
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.
That only awakened the champions as they hastily overturned the deficit, Messi driving a right-footed finish into the bottom far corner before Pulido turned Alba's cutback into his own net eight minutes later.
Left-back Alba then squared for Suarez to double the advantage in the 39th minute but there was still time for Huesca to snatch a second before the break, Gallar punishing sleepy marking with a smart first-time finish.
Barca were never unnerved and ended all doubt over the result with two more in fewer than five second-half minutes as Dembele buried his second of the season and Rakitic rifled in a splendid half-volley.
Messi waltzed through to make it a rout just beyond the hour and next turned provider for the impressive Alba in the 81st minute, before Suarez added the final gloss in stoppage time by winning and converting his own penalty.
What does it mean: Front three firing
Held to a one-goal victory at Valladolid last time out and having seen Real Madrid score four for the second match in succession on Saturday, Barca picked the right time to issue a reminder of their attacking muscle.
Star men Messi, Suarez and Dembele crucially look to be functioning on the same wavelength and, with the supply lines of Alba and Coutinho in full working order, there should be no concerns over the potency of last season's top scorers.
