The Catalans, aiming to win their first Spanish title since 2019, punished second-placed Madrid for their 1-0 defeat by Real Mallorca earlier on, opening up a wide gap ahead of their rivals.
After a tight first half Jordi Alba broke the deadlock before the hour mark, with further goals from Gavi and Raphinha helping wrap up the win.
Barcelona coach Xavi Hernandez had criticised his team in recent weeks for not killing off games after taking the lead but they did not let him down at Camp Nou.
The victory was their 10th in their last 11 league games, while Barca are now unbeaten in 15 matches across all competitions.
Barcelona have conceded just seven goals in La Liga this season, with this their 15th clean sheet.
"I think we are having a very good season, we're playing well, letting opponents have few chances," Alba told DAZN.
"We're happy, eight points clear but there's a long way to go. It's a good distance (if we) keep going like this."
Barcelona's gameplan was initially set back when captain Sergio Busquets was forced off with an ankle injury after just four minutes, replaced by Franck Kessie.
Jorge Sampaoli's Sevilla, 16th after a dismal start to the season, sat deep with five defenders and looked to frustrate the Catalans at every turn.
Moroccan goalkeeper Yassine Bounou denied La Liga's top scorer Robert Lewandowski at his near post early on, while Ronald Araujo headed narrowly off-target from a corner.
Bounou flung himself full stretch to foil a vicious Lewandowski drive from distance as Barcelona struggled to forge clear chances.
Sevilla were a little fortunate to survive the first half with 10 men when Ivan Rakitic's late lunge on Araujo was only punished with a yellow card.
Lewandowski nodded wide and Raphinha headed at Bounou at the start of the second half as the team came out with renewed vigour, keen to capitalise on Real Madrid's defeat.
Alba pounced with a tidy finish after a superb assist from Kessie, who turned well and dinked the ball into the Spaniard's path.
After Sevilla shifted to a more attacking formation Raphinha teed up Gavi for the second with a raking low pass that left the youngster with a tap-in at the back post in the 70th minute.
Raphinha provided the cutting edge on a slick 17-pass team move for the goal, in an impressive outing in place of the injured Ousmane Dembele.
Lewandowski dragged a free-kick narrowly wide as Barcelona looked to kill the game off, with the Andalusians flagging.
Alba crossed for former Leeds United winger Raphinha to finish from point-blank range for the third goal, wrapping up a satisfying day for the hosts.
Sevilla's former Barcelona midfielder Rakitic was serenaded by home fans but left dismayed at his team's lack of intent.
"I think that to be able to take something from Camp Nou, you have to be a lot braver," the Croatian told DAZN.
"You have to try, even if it's hard. Waiting so long, in the end a team like Barca will find you out. We have to get points, now."