Uruguay international Suarez scored his 101st goal for Barcelona by stroking in Andre Gomes' cutback in the 15th minute as the Portuguese midfielder recorded his first assist for the club since his 35-million-euro move from Valencia last summer.
Suarez spurned the chance to seal a hat-trick a minute later but Arda Turan mopped up after Varas had saved to score the fourth, while out-of-favour right back Aleix Vidal netted his first goal for the club in the 80th minute.
Barcelona are second in the standings, two points behind Real Madrid, who have played two games fewer and face third placed Sevilla on Sunday. Atletico Madrid are fourth on 34 points after beating Real Betis 1-0.
Barca coach Luis Enrique had rotated his side after Wednesday's 3-1 victory over Athletic Bilbao in the King's Cup, resting Neymar, Gerard Pique, captain Andres Iniesta and Sergi Roberto but still watched his side dominate Las Palmas.
"Somehow we didn't kill off the game in the first half but we were much better in the second. The entire team's defensive work was enormous."
Elsewhere on Saturday Atletico earned a third consecutive league win by beating Real Betis 1-0 in a soporific game at the Vicente Calderon thanks to a goal by Nicolas Gaitan, who stuck a foot out to divert a deflected cross in at the near post in the ninth minute in one of few openings at either end.