Valencia's stirring victory at their Mestalla stadium briefly lifted them to the top of the table before in-form pair Lionel Messi and Neymar struck in a 2-0 triumph at Rayo Vallecano, who had two players sent off, to restore Barca's two-point lead.
The Catalan club are the first La Liga team to avoid conceding a goal in their opening seven matches of the season.
Valencia, who are in the process of being taken over by Singapore billionaire Peter Lim, last won the title in 2004.
They have started the campaign in impressive form and made a thrilling start at the Mestalla to race into a 3-0 lead by the 13th minute.
Atletico centre back Miranda put through his own net in the sixth minute, Andre Gomes finished superbly after a fine run a minute later and Nicolas Otamendi nodded in at a corner to leave the champions reeling.
Mario Mandzukic pulled a goal back in the 29th minute when he followed up a Tiago effort to head home before Atletico squandered a chance for a second on the stroke of halftime.
Valencia goalkeeper Diego Alves, a penalty specialist, saved Guilherme Siqueira's weak spot kick, the 13th the Brazilian has stopped in 31 faced in La Liga.
Showing little sign of fatigue after their 1-0 win against Juventus at the Calderon, Atletico pushed hard to get back into the match but the home side comfortably held on and Alves was barely tested in the second period.
Italy winger Alessio Cerci had a miserable afternoon after coming off the bench for Atletico in the second half, picking up two yellow cards.
The second card was awarded in added time when he sprung the offside trap and put the ball in the net but the referee ruled he had used his arm to control it.
Valencia have 17 points from seven matches, with unbeaten Barca on 19.
Atletico have 14 points in third and can be overtaken by Real Madrid, Sevilla and Celta Vigo if they all win on Sunday.
"The first goal was a defensive error by a team that normally doesn't commit them," Valencia coach Nuno told a news conference.
"We have beaten a great football team, the current champions, but they are only three points," added the Portuguese, a former Deportivo La Coruna and Porto keeper who took over at the end of last season.
"We showed incredible intensity and aggression and if I was a spectator I would go away happy at having seen a good game."
Atletico coach Diego Simeone acknowledged his players had made uncharacteristic errors but said he was pleased with the work they put in to try to get back into the game.
"There are times when you lose with dignity having given everything on the pitch," the Argentine added.
"They (Valencia) are not playing in Europe this season and with the squad they have they will have to play very badly not to finish third or fourth."
Barca, who lost 3-2 at Paris St Germain in the Champions League on Wednesday, took time to get going at Rayo's Vallecas stadium in the Madrid suburbs before Messi scored a typically brilliant effort in the 35th minute.
The four-times World Player of the Year ran on to a lofted Gerard Pique pass, shrugged off a defender and sent a wonderful dinked effort over keeper Tono into the net from a tight angle on the left of the area.
Neymar added a second a minute later when he picked up a Munir El Haddadi layoff and smashed a low shot into the bottom corner.
Rayo defender Jorge Garcia Morcillo was shown a second yellow card on the hour and although Barca then took a foot off the gas they could have added to their tally several times, with Messi especially wasteful.
Substitute Javier Aquino also picked up his second yellow card for Rayo in the first minute of added time.
Chile keeper Claudio Bravo, Barca's new arrival from Real Sociedad, set a record for minutes unbeaten at the start of a La Liga season.
During the first half Bravo surpassed the previous best of 560 minutes set by former Barca and Sociedad keeper Pedro Maria Artola in 1977 and has now gone 630 minutes without conceding.
Coach Luis Enrique said the result would lift the team after Wednesday's reverse in Europe but was dismissive of Bravo's record.
"Beyond what a record means for an individual player, what is important to us is the general performance of the team," he explained.
"The only statistics that interest me are those at the end of the season which will show whether we have deserved to win the title."
In Saturday's other games, Levante let slip a two-goal lead and drew 3-3 at promoted Eibar, Malaga came from a goal down to beat Granada 2-1 and Almeria drew 2-2 at home to Elche.