Real Madrid beat Atletico Madrid in the capital derby on Saturday to move into second spot, just five points behind Barca ahead of kickoff at San Mames.
Barcelona could not return to winning ways in the league, however, with Bilbao putting on a strong performance to hold the Spanish champions to a goalless draw.
Bilbao came close to taking the lead in the 11th minute when Yuri Berchiche broke down the left before driving a low effort towards the bottom corner, but the ball moved just wide of the post.
Bilbao had another opportunity in the 17th minute when Susaeta worked a yard of space before curling a wonderful effort towards the top corner, but Barcelona goalkeeper Marc-Andre ter Stegen made a top save.
Barcelona's first real chance of the night arrived in the 22nd minute when Messi curled a beautiful pass towards Luis Suarez, but the Uruguay international just could not get the touch which would have surely made it 1-0.
Ter Stegen then had to keep out an overhead kick from Raul Garcia before Yuri had a goal-bound strike deflected wide as the match continued to produce exciting moments.
Bilbao goalkeeper Iago Herrerin had to keep out a powerful Messi drive in the 37th minute, but Barcelona struggled for inspiration in the first half and were fortunate to enter the half-time break on level terms, surviving another late scare when Raul Garcia missed the post from a dangerous area.
Barcelona were much more positive at the start of the second half, with Coutinho having a powerful strike blocked en route to goal during a period where the Spanish champions were dominating the play.
Messi was next to try his luck for the visitors in the 53rd minute, curling a free kick just over the Bilbao crossbar as the pressure continued, with Arturo Vidal also having an attempt from distance.
Bilbao had a golden chance to take the lead 25 minutes from time when San Jose found space in a dangerous position, but the midfielder's effort just missed the post. Williams then had a goal-bound flick blocked during an extremely open period of the match.
Ousmane Dembele made his recovery from an ankle problem as a 75th-minute substitute, taking the place of Coutinho, whose problems in a Barcelona shirt continued.
Williams had a wonderful chance to send Bilbao ahead in the 80th minute when the forward met a free kick from Muniain, but the ball flew just wide of the post, before the in-form Spain international fired straight at Ter Stegen from another Muniain pass moments later.
Bilbao had De Marcos sent off for a second bookable offence - deliberate handball - in the final moments, but Barcelona, who were denied a late penalty by VAR, could not find a winner as they failed to triumph for the third match in succession.
ATHLETIC BILBAO (4-2-3-1): Herrerin; De Marcos, Yeray, Martinez, Balenziaga; D Garcia, Benat (San Jose 57'); Yuri, R Garcia, Susaeta (Muniain 62'); Williams (Kodro 90')
BARCELONA (4-3-3): Ter Stegen; Roberto, Pique, Lenglet (Vermaelen 88'), Semedo; Rakitic, Busquets, Vidal (Alena 63'); Coutinho (Dembele 75'), L Suarez, Messi