The attacking duo scored a fine left-footed strike apiece before Marc Bartra headed home a third and the Uruguayan prodded in a late fourth
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 43 Barca appearances this term.
Suarez redeemed what had been a frustrating match individually with a similarly impressive second 10 minutes after half-time.
Defender Marc Bartra headed home in the 75th minute before Suarez tapped home in stoppage-time to ensure former Barca full-back Sergi suffered defeat in his first match as Almeria coach.
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.
Barca appear to be hitting their straps at just the right time, however, with an ever-improving defence keeping a clean sheet for the fourth time in five outings.
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.
There was a vital clearance from Almeria teenage debutant Antonio Marin after Messi sent Suarez scampering in behind the visiting defence and Cuesta saved with half an hour played when Xavi drilled a volley into the turf.
Murmurs of frustration were audible from the Camp Nou terraces at that stage, but Messi punctured the air of apprehension in typically majestic style.
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.
Almeria retained a threat on the break after half-time and the hosts were grateful when Suarez doubled their advantage emphatically.
Again, attacking from the right proved profitable for Barca and Suarez evaded an isolated Jose Manuel Casado to thrash a left-footed shot that Cuesta could only touch into the top corner.
Ivan Rakitic and Pedro went close as Barca revelled in a more relaxed Camp Nou atmosphere.
Bartra was allowed ample room to convert a Xavi corner with 15 minutes remaining and Messi thought he had a second, only for Cuesta to impressively keep out his 88th-minute free kick.
Suarez shrugged off brief fears that he had sustained an injury to his right leg by chalking up his double 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.