Sevilla are top on 16 points while Barcelona have 15 with Atletico Madrid but are second due to a better goal difference. Real Madrid, beaten 1-0 at Alaves on Saturday, are fourth, with 14 points.
Sevilla became surprise Liga leaders on Sunday after beating visiting Celta Vigo 2-1 while champions Barcelona drew 1-1 at Valencia thanks to another Lionel Messi strike but are still without a victory in their last four league games.
Atletico Madrid joined Barca on 15 points after scraping a 1-0 win at home to Real Betis with a late strike from substitute Angel Correa to climb above Real Madrid into third in a highly competitive campaign with the top six separated by two points.
The Catalans fell behind in the second minute at a bouncing Mestalla stadium after dreadful defending from a corner allowed Argentine defender Ezequiel Garay to stab home from close range.
Barca continued to leak chances but got a foothold in the game thanks to a superb strike in the 23rd minute from Messi, who has been in inspired form recently and delivered a performance for the ages against Tottenham Hotspur on Wednesday.
They failed to further breach a superbly organised Valencia, however, racking up a run of three draws and a defeat in four league games, their longest stretch without a win since 2016.
"This season it feels like we have to come back in every game and we are swimming against the current but we know that this is going to change," said Barca coach Ernesto Valverde.
"You always want to win and when you don't you leave with the sensation that you have dropped two points but you have to recognise that Valencia did a very good job defensively."
Sevilla are top on 16 points while Barca have 15 with Atletico Madrid but are second due to a better goal difference. Real Madrid, beaten 1-0 at Alaves on Saturday, are fourth in the standings, locked on 14 points with Espanyol and Alaves.
Sevilla midfielder Pablo Sarabia headed them towards a fourth league win in a row shortly before halftime, their task made easier when Celta's Mexican defender Nestor Araujo was sent off for two bookings in two minutes before the hour mark.
The hosts' French striker Wissam Ben Yedder doubled the lead by nudging the ball home from close range in the 61st minute, although the goal had to be verified by the video assistant referee (VAR) before it was awarded.
Celta's Sofiane Boufal scored with an impressive long-range strike in the 85th but it proved only a consolation for the mid-table visitors, who lost for the second time this term.
"I would like the season to end right now," said Sevilla coach Pablo Machin, sitting at the summit of La Liga for the first time in his career.
"We are being ruthless in front of goal and we are feeling confident. We know what we're capable of and I will try to keep this run going."
Atletico saw little of the ball against Betis but kept them at bay with shrewd defensive work and had far more chances, with Croatian forward Nikola Kalinic hitting the woodwork, although they struggled to score until Diego Simeone shuffled his pack.
Kalinic, who started in place of the injured Diego Costa, made way for Thomas Partey while Correa came on for record signing Thomas Lemar. The Argentine won possession and played a one-two with Partey before arrowing the ball home in the 74th.
"The top teams are stronger because they have great players that can come off the bench, and those substitutes at the top teams are the ones that make the difference when a game is very tight," said Atletico coach Simeone.
