Cristiano Ronaldo scored twice before injuring his leg to steer Real Madrid to a 3-0 home win over Granada on Sunday, the defending champions' first victory after three rounds of the Spanish season.
Barcelona, meanwhile, edged out Valencia 1-0 thanks to Adriano's first-half screamer to remain perfect after three games and lead the standings.
Ronaldo's double on Sunday took his tally with Madrid to 150 goals in just over three seasons. He set a club record of 46 Spanish league goals last season, second only to Barcelona forward Lionel Messi's league record of 50.
Ronaldo scored in the 26th and 54th minutes before leaving the pitch grimacing and favouring his left leg following a tackle by Borja Gomez that cost the Granada defender a second booking.
The Portugal striker chose not to celebrate his goals.
"I am a little sad. When I don't score goals I am not happy," Ronaldo said, enigmatically adding that he was displeased for "professional" reasons with "people inside the club."
When asked why after the match, Ronaldo said: "I am sad and the club knows it, that's why I didn't celebrate the goals. The people in the club know why."
Ronaldo's comments have sparked rumours in the Spanish press that he is looking to leave Madrid.
The 27-year-old Ronaldo refused to elaborate on the reasons for his displeasure with the club that spent a record 80 million pounds to secure him from Manchester United in 2009.
"I'm not going to say anything else, people know why," he said.
Ronaldo, a former Ballon D'or, denied he was angry Barcelona's Andres Iniesta beat him for this year's players' award on Friday. "It has nothing to do with it," he said. "Iniesta deserved it."
Ronaldo's outburst compounds the ongoing saga of what to do with club president Florentino Perez's other star signing, Brazil midfielder Kaka, who sought a transfer this off-season after being reduced to a bench player at best.
Yet while Kaka has been practically forgotten by Madrid coach Jose Mourinho, Ronaldo is the key player for the Spanish champions who have set winning the Champions League as their goal for this season.
With Granada down a man, Gonzalo Higuain scored in the 76th to seal the much-needed win. Madrid had only one point after the first two rounds.
"Ronaldo is an important player for us, he is our goal-scorer," Madrid defender Sergio Ramos said. "I hope he takes advantage of [this week's] international break and gets better soon."
Barcelona had the chance to decide the game after Adriano's goal, but Cesc Fabregas missed two clear chances and the hosts struggled to protect their slimmest of leads in the final minutes.
One of the few bright spots for Barcelona was former Arsenal player Alex Song, who fit in seamlessly with his new team, not erring in passes and providing a defensive presence in midfield.
Modric debuts for Madrid
Also, Athletic Bilbao beat Valladolid 2-0 for the Basques first win of the season. Sevilla drew 0-0 at Rayo Vallecano, and 10-man Levante came from behind to win 3-2 against visiting Espanyol.
In his first start for Madrid since joining from Tottenham, Luka Modric looked eager to justify his C35 million ($44 million) price tag. The Croatia playmaker drew an early save from Antonio "Tono" Rodriguez and combined well with his new teammates.
Ronaldo opened for the defending champions in the 26th when he slotted Jose Callejon's pass between Tono's legs from a tight angle on the left side of the area.
But just like in the previous two matches against Valencia and Getafe, Madrid retreated after going in front, giving Granada a chance to come forward.
"We lacked rhythm when it came to creating in attack and arriving to their area," said Ramos. "But that is normal after [the Supercup], which was a tremendous effort."
Granada forwards Floro Flores and Youssef El Arabi both came close before Ronaldo tested Tono just before the break.
Mourinho sent on winger Angel Di Maria for Callejon at the start of the second half to try to jumpstart his attack.
The Argentina international quickly responded by sliding a through ball to Ronaldo cutting toward the near post. Tono did well to block his first shot, only to see the ball fall to Ronaldo's feet for him to fire into the open net.
The Portugal striker chose not to celebrate his goals, apparently still displeased with his lacklustre play in the league.
Reduced to 10 men after Gomez's sending off, the visitors fell apart at the back, leaving Higuain alone to tap in a cross from an equally unmarked Karim Benzema and cap the victory.
Barcelona started well with Lionel Messi forcing goalkeeper Diego Alves into a diving parry to keep his early header out.
But Diego Alves could do nothing to stop Adriano 22 minutes in.
The Brazilian left back took a short pass from a corner, used one touch to gather momentum, and rocketed a right-footed shot from outside the area past the outstretched goalkeeper.
Fabregas wasted two excellent opportunities to double the lead on either side of halftime.
Messi drew the defence in and laid off for the unmarked Fabregas to send his chip shot floating by the upright. Then, Fabregas fired high after Alexis Sanchez had found him inside the box.
Valencia, which had been limited to a miss by Roberto Soldado in the first 45 minutes, provoked nerves at Camp Nou after the restart as it started to pepper Barcelona's area.
Barcelona assistant Jordi Roura, on the sideline with coach Tito Vilanova serving the first of a two-game ban for arguing with the referee, sent on Andres Iniesta, the recently crowned UEFA Best Player in Europe, for Fabregas in the 64th.
Barcelona, however, stalled in attack, apparently either tired or affected by the loss to Madrid on Wednesday.
Valencia defender Victor Ruiz came inches away from scoring the equalizer when his header just missed in the 90th.
On Saturday, it was: Celta Vigo 2, Osasuna 0; Zaragoza 0, Malaga 1; Deportivo La Coruna 1, Getafe 1; and Mallorca 1, Real Sociedad 0.
Originally scheduled for Monday, Real Betis vs. Atletico Madrid has been postponed due to international matches.