Luis Suarez opened the scoring with an improvised bicycle kick before Lionel Messi added a second with a simple finish before firing home on the volley to kill off the tie before half-time.
Barcelona dominated the ball as the game kicked off and after a three-and-a-half minute passing spell where Sevilla didn't touch the ball, Messi smashed a shot onto the crossbar from the edge of the box, leaving Sergio Rico with no chance.
Andres Iniesta then found Neymar with a neat pass on the left hand side, after another dominant passage of play, but the Brazilian's cross was easily collected by the away goalkeeper.
Luis Suarez went down in the box under the challenge of Nicolas Pareja as he looked to play a one-two with Messi but the referee waved play on, unmoved by the Barcelona appeals.
He was equally dismissive when the ball appeared to strike Samir Nasri on the arm moments later before Steven N'zonzi found a way past Javier Mascherano into the Barca box but not Marc-Andre ter Stegen who stood firm as the ball rolled just outside the right-hand post.
Ivan Rakitic headed just wide of the target on 18 minutes before the Sevilla defence combined to clear the danger after a good Sergi Roberto delivery from the right, after he had been played in behind the visiting defence by Messi.
Vitolo should have done better from a 23rd minute free-kick but he headed well over from the edge of the six-yard area from a good Nasri ball over the top.
And the miss proved costly as Suarez handed Barcelona a 25th minute lead via a cheeky bicycle kick as Gabriel Mercado's defensive touch fell kindly for the Uruguayan following a good Messi ball into the area.
Messi made it two with a simple finish from a central position after Suarez had done well to cut back an overhit low Neymar delivery after a swift counter attack where Rakitic broke forward and fed the Brazilian on the left flank.
The mercurial Messi make it three to Barcelona on 33 minutes with a volley from the edge of the Sevilla box after a corner was only half cleared by the fourth-placed La Liga side.
The hosts continued to control proceedings and Messi may well have had a third before half-time after being teed up by Neymar, but his fierce drive was well blocked.
Sevilla showed some improved signs of life as they controlled more of the ball at the start of the second half although without threatening the Barca goal, as Messi saw an audacious chipped shot collected by Sergio Rico on 51 minutes.
Clear-cut chances were few and far between for both sides inside the opening 20 minutes of the second period, but Barca continued to probe with more effectiveness.
Sergi Roberto had to be alert though to steal the ball off the toe of the advancing Joaquin Correa on the hour mark
Ter Stegen made a comfortable stop from second-half substitute Pablo Sarabia before the same player hit the side netting with an effort from wide right.
The Barca keeper then got a strong hand to a rocket of a shot from Sarabia as Sevilla upped the ante with the match winding down.
Iniesta fed Paco Alcácer with a perfectly weighted pass through the heart of the Sevilla defence but he only succeeded in firing against Sergio Rico before Rakatic hit the rebound well over the target.
With Barca content to sit back, soak up the pressure and attack on the counter, Sevilla appeared to end the match strongly, but it was more a case of match management by the home side as they ultimately saw out a comfortable 3-0 win to take the summit of the Primera Division, ahead of Real Madrid's clash with Leganés, also on Wednesday evening.