An 18th victory in 19 games for Tito Vilanova's side in an entertaining match at the Rosaleda restored their 11-point lead over second-placed Atletico Madrid, who earlier secured a 10th win in 10 home matches with a 2-0 success against Real Zaragoza.
Barca's win also extended their advantage over arch rivals Real Madrid to 18 points after the stuttering champions, mired in third, were held to a 0-0 draw at bottom side Osasuna on Saturday.
Barca have overhauled the previous record of 52 points they set two years ago under Pep Guardiola, scoring 64 goals and conceding 20, and are well on the way to breaking Real's record of 100 points for a season set last term.
The only points they have dropped were in a 2-2 draw at home to Real Madrid in October
Barca also set a new La Liga best by scoring for the 37th match in a row.
"It's incredible," Vilanova, back on the bench after undergoing throat surgery last month, told a news conference.
"It will be tough to repeat a second half like the first, it would not be normal," he added.
"We are 11 points ahead of Atletico but we still have to go to play there, we still have to play at Real Madrid.
"It's a substantial advantage but we have to keep going, there is half the season left to play."
Malaga, who play at Barca in a King's Cup quarter-final first leg on Wednesday, have the meanest defence in the league but a howler by Ignacio Camacho gifted the visitors their opener in the 27th minute.
Messi intercepted the midfielder's wayward back pass and after leaving Malaga goalkeeper Willy Caballero sprawling on the turf stroked the ball into an empty net.
It was the Argentine World Player of the Year's 28th league goal of the campaign and the ninth straight game he has scored, a personal record and one short of the La Liga best last achieved in the 1996/97 season by former Barca striker Ronaldo.
Messi sent Fabregas clear to double the visitors' lead five minutes after the break and then laid the ball into space for substitute Thiago Alcantara to add an 82nd-minute third.
Diego Buonanotte, another substitute, curled in a free-kick for Malaga a minute from time but it was far too late for the Andalusians, who slip to fifth behind Real Betis.
Resurgent Atletico go into the second half of the season with a perfect home record after Tiago and Radamel Falcao scored to help see off Zaragoza.
The comfortable victory at the Calderon means Atletico have won 10 La Liga home games on the trot for the first time in almost 40 years.
They stretched their advantage over third-placed city rivals Real Madrid to seven points and their improvement under Argentine coach Diego Simeone can be gauged by the fact that they were 23 points behind Real at the same stage last term.
Tiago nodded Atletico ahead in the 31st minute and Falcao doubled their lead from t
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