The Argentine was again a key figure as Barcelona set a new record start to a La Liga season with 13 wins and a draw from their first 14 matches, surpassing the previous best by Real Madrid in the 1991-1992 season.
The emphatic win extended the lead at the top for Tito Vilanova's team to six points, with the only dropped points in 14 games coming in the 2-2 draw against Real Madrid in October.
Messi's 84 goals in the year has him on the verge of matching the record Muller set for Bayern Munich and Germany in 1972.
Gerard Pique put Barcelona ahead after 22 minutes before Messi's first, which was sliced over the line by Bilbao defender Fernando Amorebieta on the line, before Adriano Correia hit the third on the stroke of half-time.
Cesc Fabregas then added to the deluge of goals and Ibai Gomez got a consolation before Messi struck again with a right-foot finish.
Barcelona's injury problems at the back have eased so coach Tito Vilanova was able to rest Carles Puyol and partner Javier Mascherano with Pique in the centre. With Dani Alves missing, Adriano came in at right back.
The home side began at a high tempo but while it pushed Bilbao back the visitor kept faith with Marcelo Bielsa's attacking philosophy as it looked to bring the ball out from defence.
Barca had a first sight of goal with a low drive from Andres Iniesta after 12 minutes, which 'keeper Gorka Iraizoz saved comfortably.
The Catalan side got the breakthrough after a spell of pressure.
Athletic failed to clear its lines from a corner and although Iraizoz repelled Fabregas's shot, Pique pounced on the rebound to knock it home.
Minutes later and Barca doubled the lead due in part to slack defending, which has plagued Athletic's season and one of the reasons why it appears far short of the team that reached last season's Europa League and Copa del Rey finals.
Fernando Amorebieta failed to keep tight to Messi who through on goal clipped the ball over the keeper and a despairing dive from the defender only served to help the ball over the line.
The Barca players were queuing up to score the third before the break with Fabregas having a shot saved and Messi hitting the post before Adriano burst in from the right and fired a slide-rule Fabregas pass into the roof of the net.
There was no let up after the restart and Iraizoz did well to block Messi but could do nothing to stop Fabregas who fired home an Iniesta pass inside the area.
Barca was guilty of easing off as Gomez pulled a goal back but Messi had the final say with his second.
Third-placed Real Madrid is 11 points off the pace after winning a highly-anticipated derby 2-0, ensuring second-placed Atletico Madrid's winless run in the fixture will stretch into its 14th year.
A wonderful free-kick from Cristiano Ronaldo lit up what was an otherwise disappointing first half before Mesut Ozil secured all three points with a tidy finish 25 minutes from time.
This had been billed as the biggest derby in the Spanish capital for many years given Atletico's unusually lofty position but in the most the encounter failed to live up to expectations.
Real took the lead at the Bernabeu with its first notable effort on goal as Arda Turan was penalised for handling 35 yards out and Ronaldo produced a stunning effort to score for the first time from a free-kick this season.
The game then descended into a scrappy affair before Ronaldo's ambitious strike late in the half, this time from fully 45 yards, was turned away by Thibaut Courtois.
Thankfully the pace quickened after the interval and Courtois did well once again to turn away a dangerous low cross from Karim Benzema with Ronaldo closing in, whilst at the other end Falcao pulled a shot wide from 25 yards.
Ronaldo looked the player most likely to create any sort of danger all evening, though, and he came close to a second twice in close succession just before the hour mark as he lashed a shot wide before forcing Courtois into smart stop from another free-kick.
The host's second did arrive soon after, though. Ronaldo picked out Ozil, who was free inside the area and despite a poor first touch he threaded the ball between Courtois' legs for his third goal of the season.
Ronaldo then struck the bar with yet another fierce free-kick from the edge of the area and the Portuguese was left ruing his luck again 12 minutes from time when he sprinted the full length of the field to latch onto Ozil's through-ball but hit the outside of the post from a narrow angle.
Disappointingly, Atletico produced almost nothing of note in the attacking third by way of a response as Real cruised to a ninth consecutive victory in all competitions over Los Rojiblancos.
Meanwhile, Mauricio Pellegrino was sacked as manager of Valencia after his side's 5-2 defeat at home to Real Sociedad.
The game swung on the first half dismissal of Jonas Goncalves with Valencia ahead through Roberto Soldado.
Alberto De la Bella equalised before the break and further goals came from Mikel Gonzalez, Diego Ifran, Imanol Agirretxe and Carlos Vela from the penalty spot while Soldado also got a second.
An Alberto Lopo header gave Getafe a 1-0 home win over fourth-placed Malaga, the points lifting the victor to fifth.