The win means new coach Tito Vilanova, who took over from Pep Guardiola at the end of last season, is the first to lead a side to 11 wins in their opening 12 La Liga matches since Radomir Antic achieved the feat with Real in 1991-92.
"The players made a big effort and you noticed they were tired after long trips to play with their national teams," Vilanova told a news conference.
"Leo is decisive and the great teams have great players, but he doesn't win games on his own," he added of Messi.
World Player of the Year Messi took his league tally for the season to 17 with a pair of beautifully executed finishes as unbeaten Barca moved on to 34 points from 12 matches.
Atletico had 28 points ahead of yesterday's game at Granada, while third-placed Real Madrid closed to within two of their city rivals when they crushed visiting Athletic Bilbao 5-1 in Saturday's late kickoff.
After Jon Aurtenetxe's early own goal, Karim Benzema, Sergio Ramos, Mesut Ozil and Sami Khedira were on target for Real as Jose Mourinho's side continued their recovery from a poor start to their title defence with a seventh win in eight games.
Barca, who play at Spartak Moscow in the Champions League tomorrow, 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.
Valencia beat Espanyol 2-1 at home thanks to a late penalty. - Reuters