Barcelona beat Athletic Bilbao 1-0 at San Mames after Ivan Rakitic headed in from the six yard box, running on to a perfectly-flighted cross midway through the first half.
Real Madrid secured its place at the top of the pile by beating Celta Vigo 2-1 at the Bernabeu with goals from Alvaro Morata and Tony Kroos.
Earlier on Sunday though, Las Palmas knocked in five goals against Granada which saw it edge ahead of both Real Madrid and Barcelona on goal difference.
Real Madrid has made an impressive start to the season and has now won the last 14 league games, and, according to the official website has gone unbeaten in the first home match for 11 consecutive seasons.
With Deportivo La Coruna only managing a 0-0 draw at Real Betis Friday and Leganes also playing out a goalless draw at home to Diego Simeone’s Atletico Madrid, it gave Barcelona an opportunity to join the breakaway group.
Ahead of the Sunday evening fixture, Barca manager Luis Enrique said the game at Bilbao would be a tough one.
“Playing at San Mames is one of the most difficult games we have on the road,” he said on the club’s website.
“They will make it tough for us to get the ball back when we lose it. They will create pressure up the field, and have dangerous players like Raúl Garcia and Aduriz who are strong on the ball and in the air, not to mention Inaki Williams when he’s out on the wing and has the ball in deep,” he said.
Elsewhere in the league, Villarreal plays Sevilla late Sunday.