Barcelona may have got the better of Brest in their midweek Champions League outing, but they entered this contest off the back of two disappointing league results - a 1-0 defeat against Real Sociedad and a 2-2 draw in last Saturday's meeting with Celta Vigo.
Fermin Lopez attempted to get the hosts off to a positive start against relegation-threatened Las Palmas, only to see his early effort kept out by ex-Barcelona goalkeeper Jasper Cillessen.
Barcelona threatened again in the closing stages of the first period, with Raphinha scoring from an offside position shortly before he struck the woodwork with a powerful left-foot strike.
After seeing his side draw a blank in the first period, Hansi Flick turned to Lamine Yamal at the break in a bid to find the crucial opener.
However, rather than the hosts, it was the visitors who found the breakthrough in the opening stages of the second period, with Sandro drilling a low shot past Inaki Pena to score against his former side.
Raphinha produced a superb strike to pull Barcelona level, only to see Fabio Silva net his fifth goal of the season to restore Las Palmas' advantage.
After falling behind for a second time, the Catalan side searched desperately for a second equaliser, as Ferran Torres netted an offside goal before Cillessen tipped over from Raphinha's fierce effort.
The visitors dug deep to stand firm to clinch a famous victory over the league leaders, representing Diego Martinez's fourth victory in six La Liga matches as Las Palmas boss.
Las Palmas move up to 14th place in the table, while Barcelona remain four points clear of second-placed Real Madrid.
However, the Blaugrana will be aware of the fact Real Madrid have two games in hand, while Atletico Madrid are five points behind in third spot.
BARCELONA VS. LAS PALMAS HIGHLIGHTS
Sandro goal vs. Barcelona (49th min, Barcelona 0-1 Las Palmas)
Las Palmas stun Barcelona take a surprise lead. The visitors put together a slick team move, working the ball all the way from Cillessen to Sandro. The former Barcelona forward drives a low right-foot shot into the bottom corner to score his fourth goal of the season.
Raphinha goal vs. Barcelona (61st min, Barcelona 1-1 Las Palmas)
Barcelona are level and it is that man again. Raphinha collects the ball just outside the box, before swivelling and setting the ball out of his feet to drive a left-foot shot past the despairing Cillessen to continue his impressive season.
Silva goal vs. Barcelona (67th min, Barcelona 1-2 Las Palmas)
Las Palmas are back in front. Fabio Silva latches onto to inch-perfect pass, before holding off the pressure of Pau Cubarsi to send his right-foot shot bouncing into the ground and past the helpless Pena.
MAN OF THE MATCH - KIRIAN RODRIGUEZ
Raphinha would have been named our Man of the Match if Barcelona had won, but our pick has to go to one of the key figures in Las Palmas's memorable victory.
Rodriguez produced a stellar performance in the Las Palmas midfield, with his neat pass providing the assist for Sandro's opener.
The 28-year-old also excelled in his defensive work, making two tackles, two interceptions and four recoveries while winning all five of his duels.
BARCELONA VS. LAS PALMAS MATCH STATS
Possession: Barcelona 70%-30% Las Palmas
Shots: Barcelona 27-5 Las Palmas
Shots on target: Barcelona 8-3 Las Palmas
Corners: Barcelona 7-0 Las Palmas
Fouls: Barcelona 7-11 Las Palmas
BEST STATS
WHAT NEXT?
After suffering a surprise defeat, Barcelona will have to pick themselves up for Tuesday's tricky away league clash against Mallorca.
As for Las Palmas, they will now turn their focus to their Copa del Rey away clash against fourth-tier Europa on Tuesday.