The league's leading marksman Suarez opened the scoring after six minutes, meeting Jordi Alba's cross at the far post to net his 12th goal in seven matches in all competitions and take his La Liga tally for the season to 25.
Las Palmas equalised four minutes later when striker Willian Jose beat the offside trap to latch on to Jonathan Viera's brilliant backheeled pass and steer the ball past Claudio Bravo.
Neymar restored Barca's lead in the 39th minute, and took his league tally to 18, when Lionel Messi's shot was parried by goalkeeper Javi Varas and the Brazilian netted the rebound.
"To win titles you have to suffer, (this was) a match away from home suffering ... these matches are the ones that give you the league," Suarez told Spanish television.
"What matters is for the team to keep winning. I am here to add goals and assists."
Suarez, after scoring his 41st goal of the season in all competitions, had a good chance to increase Barca's lead early in the second half but Varas made a superb stop.
Las Palmas almost levelled on the hour when Bravo saved a shot from Viera and Willian Jose put the rebound into the side-netting.
QUIET MESSI
Messi had a quiet game and Barca struggled to maintain possession. They gradually took more control in the second half after an even first 45 minutes but had to work hard to thwart the home side's counter-attacks.
Substitute Sergio Araujo, a former Barcelona B player and Argentina junior international, squandered three chances for Las Palmas near the end.
"We were up against the best team in the world. They thrive on possession and I think we were competitive but up front they make the difference," said Las Palmas midfielder Roque Mesa.
Atletico Madrid can close the gap on the runaway leaders to six points when they entertain Villarreal on Sunday. Third-placed Real Madrid, who are 10 points off the pace, travel to Malaga the same day.
Espanyol coach Constantin Galca earned a stay of execution when his side ended a run of eight matches without victory by beating Deportivo La Coruna 1-0.
Young midfielder Marco Asensio, on loan from Real Madrid, scored the only goal in the 52nd minute when he controlled a ball on his chest and volleyed past goalkeeper German Lux.
Espanyol, who edged four points clear of the relegation zone, deserved more goals and would have scored again but for a string of Lux saves.
Galca looked set to lose his job after last weekend's 2-1 defeat at Valencia, which marked Gary Neville's first La Liga win as coach, but the players rallied to the Romanian's support.
(Writing by Rex Gowar, editing by Ian Chadband)
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