Sevilla were the last side to beat Barca back in October and deservedly struck first through Vitolo.
However, as so often of late, Barca recovered from a slow start thanks to Lionel Messi's brilliant free-kick and Gerard Pique's winner early in the second-half.
Luis Enrique's men have now matched Real Madrid's record run from the 1988-89 season and in doing so moved 12 points clear of third-placed Madrid.
"We are in great form, but records don't mean anything. At the end of the day everything is judged by titles," Pique told Movistar+.
"Our season is well on track, but we need to finish it off."
Sevilla were a constant threat on the counter-attack, but should have taken the lead from a set-piece when Timothee Kolodziejczak somehow blazed over from point-blank range.
Barca nearly went in front in spectacular fashion as Messi's audacious attempt from a corner hit the post and Luis Suarez then blasted the rebound off the crossbar.
However, as ever Messi came to the fore when Barca needed him most and the five-time World Player of the Year levelled with a stunning free-kick high into the far corner 11 minutes later.
Sergio Rico prevented Messi turning the game around single-handedly before the break with a great save low to his left.
Sevilla still had the chance to take something from the game when Claudio Bravo flew from his line to block Kevin Gameiro as the Frenchman bore down on goal.
The Basques moved up to seventh in La Liga with three goals in seven second-half minutes at Mestalla.
However, Neville was furious at two strong Valencia penalty appeals that were waived away before the opener.
"I thought the referee was a joke," said the former Manchester United captain.
"I've not blamed refs in every game, but his management of the game was awful. Some of the things he did were incredible."
And Aritz Aduriz compounded a miserable afternoon for Neville by rising highest to head home Benat Extebarria's corner for his 27th goal of the season.
Villarreal moved to within two points of Real Madrid by stretching their unbeaten league run to 13 games with a comfortable 3-0 win over Levante thanks to goals from Leo Baptistao, Samu Castillejo and Adrian Lopez.
Marcelino's men should at least be assured a place in the Champions League qualifiers next season as they now lead Sevilla by 11 points in the fight for fourth place.
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