Holding a 2-1 lead, Barca was subjected to a late onslaught from the Canary Islanders, who are battling to avoid the drop from the top flight in Spain.
First half goals from Luis Suarez and Neymar, with a Willian Jose goal for the home side sandwiched between, proved enough for the Catalan giant.
But Suarez, who has moved to 41 goals for the season, admitted that tiredness after three games in a week had been a factor.
"You need to suffer if you want to win titles," he told the official Barcelona website.
"The last two away trips have presented plenty of difficulties, but we've got the three points again."
"We have played a lot of games in the last month and a half. But the players want to play and enjoy continuity. Even when we struggle in matches, we still enjoy ourselves," added the Uruguayan ace.
It was an eighth straight league win for Barca, coming hard on the heels of a tough battle at Sporting Gijon in midweek where Lionel Messi scored his 300th La Liga goal.
The Argentina ace was quieter after his heroics there and in the 6-1 rout of Celta Vigo where he famously passed from the penalty spot for Suarez to complete his hat-trick.
But Messi still had a hand in Neymar's eventual winner although Las Palmas might have drawn level in a frenetic finish as excellent goalkeeping from Claudio Bravo and wasted chances denied the home side.
Barca's closest challenger Atletico Madrid failed to close the gap on the Catalans after it was held to a 0-0 draw at home against Villarreal, while Real Madrid finds itself nine points adrift following a 1-1 draw away at Malaga.
Luis Enrique's team next faces Arsenal at the Emirates in the Champions League last 16 first leg Tuesday.
FA Cup holders held
Arsenal was held to a disappointing 0-0 home draw by second-flight Hull City in the fifth round of its FA Cup defense, admittedly with several key payers rested.
By contrast, Enrique only left out Gerard Pique of first team regulars, while Sergio Busquets was also suspended.
At least Arsenal avoided a cup upset, unlike fellow English Premier League side West Bromwich Albion, which lost 3-1 at Reading, the Championship side again enjoying a fine FA Cup run after reaching the semifinals at Wembley last year, losing to Arsenal.
The result was overshadowed by ugly scenes involving WBA's Northern Ireland international Chris Brunt, who was struck just above the eye by a coin thrown by one of the team's own fans as he went to thank them for their support at the Madejski Stadium.
Brunt said he was "disgusted and ashamed" by the incident, the English FA said it would be investigating, while Baggies manager Tony Pulis condemned it in strong terms, calling it "barbaric" and blaming social media for fueling an over reaction to defeats for sides.