Messi's brace left the 25-year-old needing just one more goal to equal Gerd Muller's record of 85 in a calendar year, set in 1972.
Two goals in three minutes - from Gerard Pique and a deflected Messi effort - midway through the opening 45 minutes put Barca firmly in the ascendancy and Adriano added a superb third in first-half stoppage time.
Cesc Fabregas notched a neat fourth soon after the break and, after Ibai Gomez had pulled a goal back with Athletic's first noteworthy attack of the match, Messi rounded things off with a brilliant fifth goal at the Nou Camp.
The emphatic win consolidated top spot in La Liga for Tito Vilanova's team, whose only dropped points in 14 games this term came in the 2-2 draw against Real Madrid in October - making their start the best ever to a top-flight season in Spain.
Athletic, languishing in the wrong half of the league table, held out for the first 22 minutes, but the writing was on the wall from the early exchanges.
Andres Iniesta brought the first save of the match out of Athletic goalkeeper Gorka Iraizoz in the 13th minute, and the Spain midfielder was at the heart of the action again soon when his shot from Messi's pass was deflected wide.
From the resulting corner - taken by Messi, on his 350th appearance for the first team - Barca went ahead.
Fabregas' shot was well saved by Iraizoz but the rebound fell kindly for Pique, who had escaped the attentions of Fernando Amorebieta and prodded home a straightforward first goal of the season.
Vilanova's side made it 2-0 from their next attack. Xavi played a fine pass for Messi, who skipped through and dinked a left-footed shot over Iraizoz, with Amorebieta only able to lift the ball into the roof of his own net from two yards out.
Messi burst through on the left side of the penalty area again in the 39th minute and unselfishly set up Fabregas, whose effort was well saved by Iraizoz low to his right.
Iniesta almost added his name to the scoresheet two minutes before the break but was forced wide and could only slice wide, and Messi went even closer moments later when his shot hit the underside of the bar and bounced to safety.
But there was still time for a third goal before the interval. Fabregas produced a slick pass from the edge of the box for the onrushing Adriano, who lashed into the roof of the net.
Athletic coach Marcelo Bielsa introduced star striker Fernando Llorente from the bench at half-time, but he could do little to change the direction of the one-way traffic.
Sergio Busquets looked to have laid on a fourth goal for Messi nine minutes after the restart, but the prolific Argentina forward's low attempt was well parried for a corner by Iraizoz.
The home fans did not have to wait much longer to see the net bulge again, though. Busquets won possession in the 57th minute and found Iniesta, whose pass with the outside of his right foot was perfect for Fabregas and he lashed home at the goalkeeper's near post.
Victor Valdes had been a virtual spectator for the first hour but was given a scare in the 64th minute when Ander Herrera's low attempt skimmed just wide of the far post.
And he was beaten soon after, when Ibai's shot from Ander Iturraspe's pass found its way through the legs of the Barca goalkeeper.
The action soon returned to the other end, though, where Pedro Rodriguez's shot was beaten away by Iraizoz in the 70th minute, and moments later Messi despatched a trademark fifth goal curling into the top-right corner.