Real Madrid beat Zaragoza 4-0 on Saturday but still remain eight points behind record breaking Barcelona who earlier won 3-1 against Celta Vigo.
Despite Madrid's recent good form it will be difficult to claw back the Catalan side, who have made their best start to a season.
Barcelona now have nine wins and a draw which beats their previous record by Louis van Gaal's 1997-98 side. Messi and company are top of the Spanish Primera Division, three points clear of Atletico Madrid.
Adriano Correia put Barca ahead against Celta after 21 minutes and while Mario Bermejo momentarily brought the visitors level minutes later, David Villa quickly restored the lead while Jordi Alba secured the win in the second half.
"What is important are the points not the record. To have 28 from a possible 30 points is not easy and shows the desire of the players. In every game we have kept going until the end," said Barca coach Tito Vilanova.
"What is important are the points not the record. To have 28 from a possible 30 points is not easy and shows the desire of the players"
Barca coach Tito Vilanova
Ahead of the game Lionel Messi showed off his Golden Boot trophy which he was presented this week after scoring 73 goals last season, while he was also the focus following the birth of his first child Thiago on Friday.
Barca were still without Gerard Pique and Carles Puyol at centre half and this time Sergio Busquets was chosen to play alongside Javier Mascherano.
Messi had the first clear chance after 18 minutes which keeper Javi Varas was equal to and the open nature of the game was shown as immediately the ball went to the other end, where Iago Aspas was denied by Victor Valdes.
Adriano Correia, joining the attack, put Barca ahead. Pedro Rodriguez got in front of full-back Roberto Iago on the right and crossed for the Brazilian to knock the ball home from close range.
The celebrations had barely finished though before Celta were level. An Alex Lopez pass split the Barca defence and Bermejo fired past Valdes on the rebound.
Barca restored their advantage with a delightful move as Villa back-heeled the ball to Iniesta, who got to the deadball line and pulled it back for Villa to score.
Right after the restart Aspas had a shot which went inches wide from a tight angle but Alba increased Barca's lead after 60 minutes. Villa flicked on an Iniesta pass to the full-back who did well to round the keeper and finish but replays showed he was clearly off-side.
Gonzalo Higuain and Angel Maria struck in a two minute blitz midway through the first half while Michael Essien and Luka Modric added another two late on as Real Madrid ran out 4-0 winners over Zaragoza.
Madrid's defensive problems eased with the return of Alvaro Arbeloa who came in on the left of defence with Marcelo and Fabio Coentrao both still injured. It freed up Michael Essien to move back into midfield where Madrid were without Xabi Alonso and Sami Khedira, suspended and injured respectively.
Zaragoza arrived at the Bernabeu with confidence restored after back-to-back wins and they made it difficult for Madrid with their organisation.
| Luka Modric scored his first goal for Madrid since moving their from Tottenham [AP]
Madrid got their opening breakthrough out of the blue from a corner.Raul Albiol leapt to power a header which Roberto got down well to save but Higuain smashed in the rebound from close range.
Zaragoza fell further behind as Di Maria had a left-footed shot from a tight angle saved by the keeper but he then cracked in the rebound.
The visitors came out for the second half with more attacking intent and seemed to take Madrid by surprise who were sitting back and allowing them to come at them.
They were mainly reduced to shots from distance and came closest to scoring with a drive by Jose Mari from 25 yards which crashed against the crossbar but Ronaldo also hit the woodwork for Madrid with a late freekick.
Essien and Modric both scored their first goals for Real, adding gloss to the result with strikes in the 88th and 91st minutes.
Valencia lifted themselves up the table with an impressive 2-0 victory over second placed Atletico Madrid. Roberto Soldado put Valencia ahead and Nelson Valdez added a second in injury time.
In the other La Liga fixture, Malaga suffered just their second loss in 16 games in all competitions when Francisco 'Piti' Medina scored twice to give Rayo Vallecano a 2-1 win at La Rosaleda Stadium.
Malaga visit AC Milan in the Champions League on Tuesday.