Atletico had earlier beaten Sevilla 4-0 to keep pace at the top and go eight points ahead of city rivals Real Madrid in third, who had lost 1-0 at Betis on Saturday.
Barca's win increases their gap over Real Madrid to 11 points, but coach Tito Vilanova does not see the league as being won so early in the season. "The league is not over, we're only a third through and Atletico are three points behind us. There is a lot to play for. We have been 11 ahead of Madrid before and we suffered a lot in the end," he said.
Alves injury scareBarca had struggled in the first half and their cause was not helped by losing Dani Alves after only 13 minutes with what appeared to be a recurrence of a recent hamstring injury.
When his replacement Martin Montoya took the pitch it meant Barca's full side had also starred for the club at youth level.
The Catalans' intricate build-up play was comfortably contained by solid defending from the home team in a tight first period. But that did not last long and Messi and Iniesta soon took charge of the proceedings.