Pedro powers Barcelona past Levante
Valencia consolidated their grip on fourth place with 31 points, a last-minute header from Juan Mata earning a 2-1 home win with 10 men over fifth-placed Espanyol.
Sevilla ended a run of five consecutive league defeats to edge out Osasuna 1-0, a header from Frederic Kanoute in the 36th minute proving enough as the home team climbed to ninth with 23 points.
Barca, without the injured Carles Puyol, suspended Gerard Pique and rested Lionel Messi, looked rusty after the league's two-week winter break.
The hosts struggled to open up Levante's massed defence until the 47th minute when Pedro kept his composure in a crowded area to score.
The second came 12 minutes later, Dani Alves breaking down the right and crossing for Spanish international Pedro to sweep in his eighth league goal of the campaign.
The crossbar denied Pedro his hat-trick and Cristian Stuani pulled one back for Levante with a superb volley 10 minutes from time.
"We knew Levante would make it tough and that they would be looking for a reaction after losing 8-0 at the Bernabeu (in their last outing)," coach Pep Guardiola told reporters after Barca took their unbeaten sequence to 24 matches in all competitions.
"We didn't play badly but we found it hard to break them open. In 50 years' time teams will still be playing with 10 men behind the ball and it will continue to be hard to beat them."
Spain midfielder Xavi made his 549th appearance for Barcelona, equalling the club record set by Migueli.
Valencia had the better of the opening exchanges at Mestalla and Aritz Aduriz powered them in front with an angled header from a corner in the 29th minute.
The visitors patiently worked their way back into the game but were lucky to level just before half-time when Valencia defender Ricardo Costa dived and headed Jose Callejon's cross into his own net.
A foolish off-the-ball elbow from Aduriz left his side with 10 men on the hour mark, and as they pushed forward Espanyol's Callejon almost put them ahead, Vicente Guaita pulling off a fine one-handed save.
Valencia's Pablo Hernandez somehow scooped over the bar from close range, but in time added on Spain winger Mata raced into head home from a well-worked move, though television replays showed he was in an off-side position.
"It was a very even game but we had the luck to score in the last move," Mata told Spanish television. "They are three very important points for us to secure us in the Champions League places."
In other games, Deportivo La Coruna were 2-1 winners at Athletic Bilbao, who stayed eighth with 25 points, and Malaga dragged themselves out of the bottom three with a 2-1 victory at Sporting Gijon.