A brace from Luis Suarez and one each from Lionel Messi, Arda Turan and Aleix Vidal secured a comfortable win for the Catalan giants, who have closed the gap on their bitter rivals to just two points, but Luis Enrique's side have now played two more games than the unbeaten league leaders.
As for Las Palmas, head coach Quique Setien recalled his big guns, including Jonathan Viera and Kevin-Prince Boateng, following their 3-2 success over Atletico Madrid in the Copa del Rey during the week.
Barcelona went after the away side from the very first whistle and Las Palmas midfielder Roque Mesa picked up the game's first yellow card inside the opening two minutes when he hauled Luis Suarez to the deck on the edge of the box. Messi was again on set-piece duty for the Catalan giants, but this time the Argentine's effort was too high.
Enrique's side made the breakthrough in the 14th minute, however, when Gomes beat Las Palmas's offside trap and delivered a low cross into Luis Suarez, who smashed the ball passed Javi Varas for the opening goal.
Las Palmas's first opportunity of any note arrived in the 19th minute when Nabil El Zhar delivered a dangerous cross towards the far post, where Boateng was waiting, but the number seven's effort was wide of the post.
Rafinha should have doubled Barcelona's lead in the 21st minute after Messi found the Brazilian midfielder in space, but his effort was wide of the far post as chances continued to arrive in what was an open and entertaining game of football.
Four minutes later, the hosts had another wonderful opening when Luis Suarez delivered a cross into Gomes, who only had to tap home from close range, but Las Palmas goalkeeper Varas saved from point-blank range.
Gomes could have had a hat-trick in the first period and passed up another clear chance in the 32nd minute - firing wide after being released by Sergio Busquets inside the box - before Messi missed the far post with a low effort after Varas had failed to collect an attempt from Turan.
Messi went head to head with Varas on two more occasions in the latter stages of the first period, and the Las Palmas goalkeeper won both battles as he kept out a dipping free kick from the Argentine before denying him from a one-on-one.
Messi had the first real chance of the second period in the 51st minute, but the Argentine fired over the crossbar from a wide angle. He was not to be denied though and found the back of the net less than 60 seconds later after Varas had palmed a Rafinha cross straight into his path.
Las Palmas were still a threat though, and Boateng picked up a yellow card in the 55th minute for a bizarre flying handball as the former AC Milan midfielder desperately tried to get his team back in the match.
Barcelona scored their third and fourth within the space of two minutes, however, as Luis Suarez curled one into the bottom corner for 3-0 before Turan dispatched from close range after Varas had kept out another effort from Suarez.
The home side were utterly dominant as they went in search of more goals and Varas again had to be alert to keep out a close-range Messi header in the 66th minute during a period where both managers made changes. Indeed, there was to be no hat-trick for Suarez as Paco Alcacer was introduced for the Uruguayan in the 68th minute.
Boateng had a super chance to put Las Palmas on the board 15 minutes from time after breaking into the Barcelona box, but the Ghana international could not find a route past Marc-Andre ter Stegen.
Barcelona then scored their fifth in the 80th minute when Alcacer delivered a terrific cross into Vidal and the right-back, who had looked set to leave Camp Nou this month, found the bottom corner with a smart finish.
The home side continued to search for more goals in the latter stages as Las Palmas dropped deeper and deeper, but it ended 5-0 as the Spanish champions returned to winning ways in impressive fashion.
Next up for Barcelona is a trip to Real Sociedad on Thursday night in the first leg of their Copa del Rey quarter-final, before the Catalan giants return to league action away to Eibar next Sunday night.
Las Palmas, meanwhile, will attempt to return to winning ways in the league when they host Deportivo La Coruna on Friday night.