Messi went into the contest nursing an injury to his right foot but illuminated a largely forgettable first half with a sumptuous strike – his 44th goal in 43rd Barca appearances this term.
Suarez redeemed what had been a frustrating match individually with a similarly impressive second 10 minutes after half-time.
The Andalusian side dispensed of Juan Ignacio Martinez after a run of seven winless games, though Sergi may well target Saturday's fixture against fellow strugglers Granada as a chance to turn their fortunes around.
Though ultimately comfortable, Barca were made to sweat through much of the first half as Suarez wasted a free header from a seventh minute corner before Messi nodded Dani Alves' cross into the arms of goalkeeper Julian Cuesta.
Barca struggled to create early clear openings despite dominating possession and Wellington Silva was only denied by a last-ditch intervention from Pedro – the winger's best contribution coming in defence despite being brought in to replace the off-form Neymar.
Cutting in from the right flank, Barca's talisman skipped past Edgar Mendez's challenge and curled a beauty into the far corner from the edge of the area.
Suarez shrugged off brief fears that he had sustained an injury to his right leg by chalking up his brace in stoppage time, completing a simple finish from Pedro's low cross moments after Almeria midfielder Thomas Partey had a spectacular volleyed effort disallowed - a moment to encapsulate the struggles that Sergi must turn around.
