Real Madrid's early-season woes deepened when they lost 2-1 at home to La Liga champions Atletico Madrid, while substitute Neymar struck twice in Barcelona's 2-0 win against visiting Athletic Bilbao on Saturday.
In their last league outing at the end of August, Real let slip a two-goal lead and lost 4-2 at Real Sociedad and it was another disappointing display from the European champions, who have spent heavily to bolster their star-studded squad after winning a 10th continental crown last term.
Tiago beat Karim Benzema to the ball at a corner to head Atletico in front in the 10th minute before Cristiano Ronaldo levelled for the hosts with a 29th-minute spot kick after being brought down by Guilherme Siqueira.
Real dominated for long periods without threatening a typically dogged Atletico side and paid dearly for failing to press home their advantage when substitute Arda Turan swept the ball low past Iker Casillas with about 15 minutes left.
"We play as a team, we all give 100 percent and it came off superbly," Tiago said in an interview with Spanish television broadcaster Canal Plus.
"It is not easy to win here and it was a demonstration of the strength of this side," added the Portuguese midfielder.
The Real fans made their displeasure plain at the final whistle and a cacophony of whistles rang out around the Bernabeu stadium as the players trudged off.
There were calls in one section of the crowd for president Florentino Perez to resign, while goalkeeper and captain Iker Casillas was also whistled by some of the home support.
"We have to lift ourselves and fight and prepare for the next game," Real's Portugal centre back Pepe told Canal Plus ahead of Tuesday's Champions League Group B opener at home to Swiss side FC Basel.
"It is hard to find explanations immediately after the end of the game," Pepe added.
"As always, they scored against us from a set piece. We work at it but perhaps we are not focused enough to stop these kinds of balls."
Atletico's latest win over their crosstown rivals, the first time they have secured consecutive victories against Real at the Bernabeu, suggests they are genuine contenders for silverware again this season despite losing top scorer Diego Costa to Chelsea.
Atletico lost 4-1 to Real in last term's Champions League final but gained a measure of revenge by beating their local rivals 2-1 on aggregate in the season-opening Spanish Super Cup.
Real, meanwhile, are left wondering whether the decision to sell midfielders Xabi Alonso and Angel Di Maria and replace them with Toni Kroos and James Rodriguez was the right one.
The pacy Di Maria was one of the team's best performers in recent seasons, while the experienced Alonso gave the team solidity and control in midfield.
Neymar came off the bench for Barca in the earlier kickoff and produced two exquisite finishes from brilliant Lionel Messi assists to secure a 2-0 win at home to Bilbao and maintain their perfect start to the campaign.
Barca were much the superior side at a sun-drenched Nou Camp but were unable to make a breakthrough until Neymar ran clear on to Messi's threaded pass and dinked the ball past onrushing keeper Gorka Iraizoz for a 79th-minute lead.
Five minutes later, Messi made one of his scintillating runs down the right and clipped the ball across to the unmarked Neymar, who had time to steady himself before sidefooting clinically into the bottom corner.
The Brazil captain is coming back from an ankle injury and new Barca coach Luis Enrique held him back until the 63rd minute, when he replaced teenage Spain forward Munir el Haddadi.
Barca, seeking to improve on last season's second place finish to Atletico, were the only team to win their opening two games and top the table with a perfect nine points and no goals conceded.
"We struggled a bit to put the ball in the net but we managed a win that puts us in a strong position," Barca keeper Claudio Bravo, who joined in the close season, told reporters.
With just over 80,000 fans thronging Barca's giant stadium, Messi was in the starting lineup having shaken off the muscle injury that prevented him joining up with Argentina for international duty this month.
The Argentina captain was joined in attack by Pedro and Munir, while playmaker Andres Iniesta also returned from injury to captain the side.
The Barca players were wearing the yellow and red of the Catalan flag to mark the region's national day on Sept. 11 and there was a festival atmosphere as the home side carved out much the better chances in the first half.
Iraizoz pulled off three fine stops to deny Pedro, Ivan Rakitic and Munir, while at the other end Ander Iturraspe's low shot in the 28th minute was the first on target Barca had conceded in La Liga this season.
The second half was more of the same, with Iraizoz again doing well to deny Jordi Alba before an unmarked Munir, who earlier had the ball in the net but was ruled narrowly offside, headed straight at the keeper when well placed.
Bilbao have not won at the Nou Camp since the 2001-02 season and were looking good for a point until Neymar gave Barca some extra zip in attack.
His connection with Messi did not function as well as hoped last term in his debut season in Spain but on the evidence of Saturday's game the South American pair are starting to gel in an ominous sign for Barca's rivals.