Coutinho gave the reigning champions the lead inside two minutes with a fine finish after being played in by Messi.
The Argentine slid a clever reverse pass through to the former Liverpool man, and he clipped a lovely finish home from about 15 yards out.
Next it was Luis Suarez's turn to prove, playing Messi in down the right hand side before the Barcelona captain did the rest.
He sold one defender with the drop of a shoulder and curled a lovely finish into the bottom corner, putting his side two to the good.
Sevilla had almost no answer to Barcelona in the opening stages, and it could be a long night for the side from Andalucia.