rounds surpassed Madrid's 12 wins and two draws to begin the 1991-92 campaign.
The leader's milestone, unmatched in 81 previous seasons, came in the first year under coach Tito Vilanova, who took over from Pep Guardiola in the offseason after four campaigns as his assistant.
"I'm very happy for the performance of my players and for having achieved the record," said Vilanova. "It's good to have won so many games, but I am even happier that even winning 5-1 we were still looking for a sixth goal until the end.
"I'm sure that we will compete for titles this season."
Barcelona led 3-0 by halftime thanks to goals by Gerard Pique, Messi and Adriano. Cesc Fabregas and Messi scored after halftime.
Messi's 11th double of the season left him one goal shy of Gerd Mueller's record of 85 for club and country in a calendar year, set in 1972.
The 25-year-old Messi, who could become the first player to win the FIFA world player of the year award four times, has scored 28 times this season, including a league-leading 21 goals.
Madrid's ninth straight win in the Spanish capital's biggest derby kept alive its run of not losing to Atletico in 24 straight games, dating back to 1999.
Atletico entered the game on its best start ever with 11 wins in 13 rounds. But any hopes of ending years of misery were crushed when Cristiano Ronaldo scored an exquisite free kick in the 16th minute.
"We are feeling down," said Atletico coach Diego Simeone, who denied that his team has a psychological block when it comes to facing Madrid. "They scored on their first chance. Until that goal my team was playing well, but we couldn't go forward in attack and that's why we lost the game."
The match at the Santiago Bernabeu featured more hard fouls, petty scuffling, and bad tempers than beautiful play.
Neither team shined, but Atletico was as nervous and apparently intimidated as ever as it consistently rushed its passes in midfield, which inevitably ended in Madrid charging the other way with the ball.
Atletico remained in second place with its second loss of the season. But Barcelona is six points clear, as third-place Madrid closed to within five of its city rival.
After Madrid goalkeeper Iker Casillas saved Radamel Falcao's only clear chance to score, Atletico winger Arda Turan conceded a free kick outside his area by handling the ball.
Ronaldo stepped up and struck an unstoppable dipping blast that left the diving Thibaut Courtois with no chance in goal.
Madrid had no trouble halting Atletico's occasional surge forward, and a poor clearance by Miranda in his own half led to Mesut Oezil scoring Madrid's second goal in the 66th from a pass by Ronaldo.
Only the woodwork saved Atletico from a rout as Ronaldo hit the goal-frame twice before the final whistle.
"We have to keep going ahead three points at a time," said Madrid midfielder Xabi Alonso.
Barcelona turned to a set-piece to break through with its passing game temporarily held in check early at Camp Nou.
Pique pounced on the rebound of Fabregas' shot from a corner that goalkeeper Gorka Iraizoz did well to block to open the scoring in the 22nd.
Messi then struck to double the advantage three minutes later when he took Xavi Hernandez's pass, dribbled across the box, and flipped a shot over Iraizoz that scrambling defender Fernando Amorebieta couldn't keep out of the net.
Bilbao's defensive discipline crumbled, and moments after Messi hit the crossbar, Fabregas threaded a pass through the defense for the streaking Adriano to blast over Iraizoz in first-half injury time.
Fabregas took his goal in the 57th from a pass by Andres Iniesta.
"We enjoyed the game a lot and we each gave it our all," said Fabregas. "We are completely worn out, but it was well worth it."
Ibai Gomez got Bilbao's consolation goal in the 65th.
Messi recorded a double for the fifth straight game five minutes later when he evaded a defender with one touch before curling a strike into the far side of the net.
Also, Valencia fired coach Mauricio Pellegrino after losing 5-2 at home to Real Sociedad with all the visitors' goals coming after Jonas was red carded in the first half, leaving Valencia with 10 mean.
Getafe, meanwhile, beat Malaga 1-0 for its third consecutive win.