Messi found spaces hard to come by in a tight first half and it was Suarez who opened the scoring after he played a one-two with Philippe Coutinho and advanced into the box and kept his balance to beat Eibar goalkeeper Asier Riesgo with an excellent left-footed finish.
Barca wrapped up the three points in a flurry of chances early in the second half.
Tthe Catalans doubled their lead after Coutinho and Suarez combined for Messi, who slotted low past Riesgo and inside the far post to net his 400th goal in La Liga.
That new milestone for the Argentine was greeted with big cheers at Camp Nou, but there was more to come just a few minutes later as a Sergi Roberto throw-in from the right found Suarez and the Uruguayan set off on a diagonal run which culminated in him finding an angle to fire past Riesgo and make it 3-0.
Substitute Pablo De Blasi tested Marc-Andre ter Stegen at the other end, but Barca also missed chances to add to their lead and ran out 3-0 winners.
Ernesto Valverde’s side now have 43 points after 19 rounds of La Liga, with Atletico in second on 38, Sevilla on 33 and Real Madrid (in action later against Betis) on 30.
SourceL Evening Standard