Visitors Barca dominated proceedings early on at Estadio Ramon Sanchez Pizjuan, and they were rewarded when Xavi Hernandez curled home a free-kick to make it 1-0 in the 18th minute.
It was 2-0 seven minutes later, with Lionel Messi playing the ball through the legs of Emir Spahic, before beating Sevilla goalkeeper Andres Palop with an exquisite chip.
Rayo Vallecano were comfortable 3-0 winners at home to fellow promoted side Real Betis.
Goals from Emiliano Armenteros, Diego Da Silva Costa and Raul Tamudo, all in the second half, did the damage for hosts Rayo at Campo de futbol de Vallecas.
The other team to be promoted last season, Granada, were also victorious, as they downed Sporting Gijon 2-1 at home.
First-half goals from Carlos Martins and Guillherme Siqueira earned Granada an early 2-0 lead, with Adrian Colunga pulling one back for the visitors in extra-time.
Granada finished with 10 men after goal-scorer Martins received a straight red card in the 94th minute.
Bottom side Real Zaragoza passed up the chance to record a much-needed win, as they drew 1-1 at home to Osasuna.
Strugglers Zaragoza took the lead through Helder Postiga in the 86th minute of the match, but surrendered their advantage just 60 seconds later, with Roversio levelling for the visitors.
Inigo Martinez's own-goal gifted Real Sociedad a 1-0 win in their match away to Getafe.
