Barcelona left it late to beat Granada 2-0 and extend their perfect record, while there were victories for Real Zaragoza, Celta Vigo and Real Betis.
Barcelona have been in fine form in winning their opening four Primera Liga games of the season, but they were made to work hard for a UEFA Champions League win over Spartak Moscow in midweek and were given another tough test by Granada.
Granada withstood an onslaught to remain on level terms until deep into the second half, producing a spirited defensive performance and even coming close to taking the lead on the counter-attack.
Lionel Messi had been denied on multiple occasions by the inspired heroics of goalkeeper Tono and it looked like the game would end in a frustrating stalemate, but Xavi came up with a moment of magic to smash a brilliant finish in off the underside of the crossbar with three minutes remaining.
Borja Gomez then turned in an own goal following fine play from Messi to give Barca a second and stretch their lead at the top of the table to
Real Zaragoza recorded their first win over Osasuna in five years with an entertaining 3-1 victory at La Romareda.
Helder Postiga had given the hosts an early lead with a neat finish after four minutes, but Emiliano Armenteros brought Osasuna level with his first goal for the Navarrans 25 minutes later.
The game swung back in Zaragoza's favour, though, moments before the break when Victor Rodriguez's cross was deflected into his own net by David Timor and Apono secured all three points from the penalty spot 19 minutes from time.
A fourth defeat in five games leaves Osasuna rooted to the foot of the table and they were left to rue their profligacy in front of goal as they created just as many chances as the hosts throughout the 90 minutes.
On-loan Arsenal striker Park Chu-Young came off the bench to score the winner as Celta Vigo defeated Getafe 2-1 at Balaidos.
Celta missed a host of opportunities to take the lead in the first half but eventually went in front after the break as Michael Krohn-Dehli released Augusto Fernandez to fire home.
Going behind seemed to arouse Getafe from their slumber and they responded immediately as Abdel Barrada rattled in his third goal in four games two minutes later.
But it was the Korean who had the final say when he converted at the back post from another Krohn-Dehli cross 22 minutes from time, with the visitors ending the game with 10 men as Alexis was sent off for striking Hugo Mallo.
Real Betis responded to the pressure placed on them by club president Miguel Guillen with a narrow 1-0 win over 10-man Espanyol.
Guillen turned up the heat on coach Pepe Mel this week by declaring Betis should look to improve on last season's 13th-placed finish.
Mel brought in eight new players over the summer and Guillen felt that, after two wins from their first three games, they should be aiming for the top half.
And that looks a distinct possibility after Junior Paulao's goal was enough to make it three wins from four games against lowly Espanyol.