Having seen Real Madrid go top on Saturday, the Catalan side joined their bitter rivals and also Atletico Madrid thanks to a come-from-behind victory on a torrid night.
With heavy rain making passing football near-impossible, Barcelona found a way with Alexis Sanchez's botched header, Lionel Messi's brace and Cesc Fabregas' late goal washing out Alberto Moreno's opener.
Despite the comfort of the scoreline, Barca had to survive their post being hit when a goal down and also had to rely on Victor Valdes to make a number of impressive saves.
There was nothing he could do when Moreno opened the scoring with 15 minutes gone, though, with the Spain international's shot getting a deflection and wrong-footing him.
It was so nearly two shortly after as Ivan Rakitic's cross was flicked by Carlos Bacca, with the post saving the visitors.
The sides traded long-range efforts after that, before Rakitic shot just wide after a fine Sevilla move.
Barca then made the most of their good fortune as Alexis, in an offside position, turned his back on Messi's cross but turned around to see he had diverted it into the net via his shoulder and neck.
And, as Barca are capable of, they made it two before the break as Messi finished off a thrilling counter-attack, taking in Pedro's ball from the left and drilling a fine shot across a stunned Antonio Beto.
It made for a half-time break Sevilla had not expected but they could have been level after it, only for Machin Vitolo to slide the ball across Valdes' goal after he had got clean through via some fine harrying of Gerard Pique.
Sensing the need for a third, Barca pressed and Alexis' cross deserved better than no-one getting a touch, before Valdes really excelled himself.
He pushed away Bacca's edge-of-the-box shot before springing up to deny Kevin Gameiro on the rebound.
The value of his save was then made clearer as Messi finished off another counter, receiving an Andres Iniesta pass in the tightest of situations and getting the ball out of his feet well enough to put a shot beyond Beto from 18 yards.
The goal deflated Sevilla and they were put to bed with four minutes left as Fabregas ran on to Alexis' ball from the right and produced the coolest of chips to finish things off.