The Argentine World Player of the Year, who struck either side of Alex Song's debut goal for the club, took his league tally to 17 as unbeaten Barca moved on to 34 points from 12 matches.
Atletico can trim the gap back to three with a win at Granada on Sunday.
After sending an early shot narrowly wide, Messi opened the scoring in the 16th minute at the Nou Camp when he picked up Jordi Alba's pass and clipped the ball into the bottom corner.
Zaragoza pulled a goal back eight minutes later when a Francisco Montanes shot took a slight deflection off Carles Puyol, back in central defence after injury, and flew past Victor Valdes.
Song, who joined from Arsenal in the close season, thumped a Messi pullback through a crowd of players into the net to restore Barca's lead in the 28th minute and Messi curled in his second to kill off the game on the hour.
It was his 78th goal of 2012 for club and country - 66 for Barca and 12 for Argentina - and he is closing in on the record for a calendar year of 85 set by German Gerd Mueller in 1972.
Barca, who play at Spartak Moscow in the Champions League on Tuesday, have dropped points only once in La Liga this term, a 2-2 draw at home to Real.
Malaga extended their winless run in La Liga to three matches when they were held to a 0-0 draw at struggling Osasuna.
Manuel Pellegrini's side, who are through to the last 16 of the Champions League with two games to spare, stay fourth on 19 points but Real Betis and Levante can climb above them on Sunday with wins at Sevilla and Deportivo La Coruna respectively.
Roberto Soldado's 89th-minute penalty gave erratic Valencia a much-needed 2-1 success at home to Espanyol, who had Hector Moreno and Sergio Garcia sent off for protesting the referee's decision to award the spot kick for a Moreno handball.
Jonathan Viera ran onto a loose ball and sidefooted past Cristian Alvarez to put Valencia ahead in the 16th minute in an ill-tempered match at the Mestalla, which as well as the two straight reds saw 11 yellow cards.
Samuele Longo scooped the ball over Diego Alves from close range to level 15 minutes later.
Valencia are sixth on 18 points, while Espanyol slip below Osasuna to the bottom of the table, making it increasingly likely coach Mauricio Pochettino will lose his job.