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The victory keeps Josep Guardiola's team 12 points ahead of Real Madrid, who scored a 1-0 home win against Racing Santander on Saturday.
Real, for their part, are looking solid in second place, thanks to the defeats suffered by Sevilla and Valencia.
Sevilla surprisingly lost 2-1 at home to crosstown rivals Betis on Saturday, Valencia crashed 1-0 away to Osasuna on Sunday.
Osasuna are now fourth from bottom, with Numancia, Espanyol and Mallorca below them.
Atletico Madrid, meanwhile, were moving up to sixth, with a 3-0romp away to Recreativo Huelva, in what was a dream start for new coach Abel Resino.
Atletico's South American strikers Diego Forlan and Sergio Aguero tore Huelva apart in the first half, with Forlan scoring two and Aguero one.
Malaga are level with Atletico on 35 points after coming from behind to beat Almeria 3-2, with two late goals from veteran Salva.
Later on Sunday, Barcelona made short shrift of Gijon.
Samuel Eto'o opened the scoring in the 23rd minute, culminating from close range a textbook counter-attack launched by Andres Iniesta and continued by Thierry Henry.
Five minutes before half-time, Eto'o made it 2-0 with a fierce drive, after being played through by the unusually quiet Lionel Messi.
Eto'o is top of the Liga scoring chart with 21 goals, four ahead of David Villa of Valencia.
In the 66th minute, Iniesta set up Daniel Alves to score the third goal with a powerful near-post drive.
Four minutes later Kike Mateo pulled a goal back for Gijon with a low drive.