Atletico Madrid kept pace with the leaders three points back in second with a 2-0 success at home to Getafe, while third-placed Real Madrid were indebted to goals from a wounded Cristiano Ronaldo and substitute Alvaro Morata in a 2-1 win in almost unplayable conditions at waterlogged Levante.
Deployed at centre-forward in the absence of injured strikers Karim Benzema and Gonzalo Higuain, Ronaldo sustained a nasty cut above his left eye when he was caught by David Navarro's elbow in the opening minutes of the match in Valencia.
After having it taped up on the side of the pitch, he popped up at the far post in the 21st minute, controlled a looping ball on his thigh and crashed a superb volley high into the net.
The Portuguese was replaced at halftime by centre-back Raul Albiol as a precaution and Levante substitute Angel Luis Rodriguez levelled in the 62nd minute before Xabi Alonso had a penalty saved by home goalkeeper Gustavo Munua.
An unmarked Morata nodded in Alonso's inswinging free-kick six minutes from time moments after entering the fray and Jose Mourinho's side stayed five points behind Atletico, whom they host on December 1.
Unbeaten Barcelona's 10th victory in 11 La Liga matches, in which Xavi and Cristian Tello also scored, and haul of 31 points equalled the best start to a league campaign achieved twice by Real - in the 1968/69 and 1991/92 seasons.
However, Barca coach Tito Vilanova will be wondering how inept defending allowed Mallorca to score twice early in the second half to get back to 3-2 before Messi struck his second of the night with 20 minutes left.
It was the World Player of the Year's 76th goal of 2012 for club and country - 64 for Barca and 12 for Argentina - and he is closing in on the record for a calendar year of 85 set by German Gerd Muller in 1972.
The 25-year-old has 15 in La Liga this season, three ahead of Ronaldo.
LITTLE MISTAKE
"The team is in a situation right now when any little mistake costs you a goal," Vilanova told a news conference.
"Maybe one goal against would have been a just reflection of how the match went but not two," added Pep Guardiola's former assistant, who stepped up to take the top job at the end of last season when Guardiola quit.
Barca, whose only dropped points came in October's 2-2 draw at home to champions Real, took a 28th-minute lead at Mallorca's Iberostar stadium when Xavi left goalkeeper Dudu Aouate rooted to the spot with a sumptuous free-kick.
Messi, who had his new-born son's name Thiago written on his boots, made it 2-0 when Aouate let his low drive squirm past him in the 44th minute and Tello cut in from the left and curled into the far corner a minute later.
Mallorca kept plugging away and were rewarded 10 minutes into the second period when Javier Mascherano surrendered possession on the right and the ball eventually fell to Michael Pereira who smashed it past Victor Valdes.
Victor Casadesus scored from the spot two minutes later after a Sergio Busquet
