A 5-0 win at Levante saw Barcelona's perfect start to the season continue, while Villarreal came from two down to beat Rayo Vallecano 4-2.
Luis Enrique's start to life as Barca coach has seen the team collect four successive league wins without conceding a single goal and, although Neymar was initially wasteful, they romped to victory on Sunday.
The Brazilian spurned several chances in the first half at Ciudad de Valencia, before finally finding the breakthrough in the 34th minute.
Loukas Vyntra then picked up a red card for fouling Lionel Messi in the area just before half-time and, although the Argentinian missed the target with his spot-kick for the first time in his La Liga career, Ivan Rakitic emphatically made sure Barca held a 2-0 lead at the interval.
Neymar was unhappily withdrawn just after half-time following a knock to his ankle, but his replacement Sandro Ramirez swiftly gave Barca a three-goal lead.
A Pedro tap-in and a clever Messi chip after Jesus Fernandez's dreadful attempted clearance gave the scoreline a resounding look in the final 30 minutes, ensuring Barca ended the weekend where they started it; at the top of the table.
Villarreal were forced to do things the hard way as they came from two goals behind to beat visitors Rayo 4-2 at El Madrigal.
Gael Kakuta headed the away side into a 22nd-minute lead and they doubled their advantage seven minutes later as Alberto Bueno tapped in after Sergio Asenjo could only parry a Leo Baptistao effort.
The Villarreal fightback started in the 33rd minute, though, as Javier Espinosa finished off a fine move by the hosts.
Mateo Musacchio headed Villarreal level with just under 30 minutes to go and Luciano Vietto netted his first goals from the club to secure victory.
The 20-year-old Argentinian replaced Espinosa just before the hour and his impact was telling, firing Villarreal ahead in the 74th minute, before completing the scoring in the dying stages with an easy finish.
Sevilla went to the top of the league for a couple of hours after beating hosts Cordoba 3-1 in the visitors' first Andalucian derby of the season.
Unai Emery's men dominated for much of the game and, although Borja Garcia scored late on for the hosts, the Europa League champions claimed victory thanks to a Carlos Bacca double and a header from Stephane M'Bia.
The day's early kick-off saw Almeria pile even more pressure on to Real Sociedad coach Jagoba Arrasate with a 2-1 win at Anoeta.
An Alberto de la Bella own-goal gave the visitors the edge in the first half and Mauro dos Santos doubled their lead just after the break.
Sebastian Dubarbier's red card for a second caution in the 79th minute gave Real hope, but they were unable to salvage a point despite Gonzalo Castro's late consolation.