Ernesto Valverde's side were made to battle for their point in an industrious encounter, as Lionel Messi grabbed his first-ever away goal on the island in what turned out to be a frustrating night for the visitors.
The Argentine playmaker opened the scoring with a memorable free kick, before being left frustrated by Jonathan Calleri's controversial penalty early in the second half, which helped to boost the hosts' growing survival hopes.
Ahead of a vital clash with second-placed Atletico Madrid at the weekend, Valverde decided to start both Messi and Luis Suarez and the pair almost started with devastating effect, only for Messi to underhit his pass to Suarez with the attackers bearing down on a stranded Leandro Chichizola.
Las Palmas pressed with great intensity in the first half and made Barca work for every yard, but Messi soon went close again when he saw his bending free kick tipped around the post by a diving Chichizola in the home goal.
The keeper was to offer less resistance next time around, however, as Messi curled an unerring set piece into the far corner to make it 1-0, after Joaquin Navarro had initially brought the playmaker down on the edge of the box.
The home side were able to offer little going forward in the opening half, but Jonathan Calleri almost caused an issue when he broke between Sergi Roberto and Marc-Andre ter Stegen, only to fluff his lines and send an effort wide of the target.
The second period started in bizarre fashion as the referee gave a controversial penalty against Barcelona, who were penalised for a supposed handball from Lucas Digne as the ball ricocheted back off the post, much to the dismay of most of the players on the pitch.
The decision provided Calleri with the opportunity for Las Palmas to level from the spot, which he took with consummate ease courtesy of an adroit finish into the top corner.
Valverde soon introduced Philippe Coutinho and the Brazilian almost made an instant impact when he slipped in Messi, although the Argentine was denied a route to goal by a standout recovering challenge from Matias Aguirregaray.
The visitors continued to push for a winner but Las Palmas defended defiantly for the final 20 minutes, earning themselves a memorable point to help strengthen what could become a remarkable push to survive relegation this term.
The draw now leaves league leaders Barca just five points clear of Atletico ahead of the clubs' crucial clash at Camp Nou on Sunday.
LAS PALMAS (4-2-3-1): Chichizola; Aguirregaray, Navarro, Galvez, Castellano (Michel 76'); Etebo, Gomez (Aquilani 70'); Halilovic, Tana, Samperio; Calleri
BARCELONA (4-4-2): Ter Stegen; S. Roberto, Umtiti, Vermaelen, Digne; Paulinho (Rakitic 63'), Busquets, Iniesta (Dembele 75'), Vidal (Coutinho 57'); Suarez, Messi