* Fabregas scores two in Barca's 4-1 win at Betis
* Messi substituted with hamstring problem
* Atletico held 1-1 at Villarreal after two own goals (Adds Fabregas, Simeone quotes)
By Mark Elkington
MADRID, Nov 10 (Reuters) - A Cesc Fabregas double helped Barcelona maintain their unbeaten start to the season with a 4-1 win at bottom side Real Betis to move three points clear in La Liga on Sunday although they lost Lionel Messi to injury.
Barca now have 37 points from 13 games ahead of second-placed Atletico Madrid, who were denied a couple of hours on the summit when Juanfran put the ball into his own net late on in a 1-1 draw at Villarreal, who also scored an own goal.
Barcelona midfielder Fabregas struck twice in the second half after quickfire goals from Neymar and Pedro in the 35th and 37th minutes had settled the champions, who required three top class saves from Victor Valdes before they took control.
Messi had been replaced by Andres Iniesta after 21 minutes as the World Player of the Year called for a change with a hamstring injury before Fabregas squared for Brazil forward Neymar to sidefoot the opener into an empty net.
Pedro's goal two minutes later was outstanding as the Spain forward burst forward from his own half, raced into the area and curled a shot inside the far post.
Betis struck the post early in the second half, but a sublime pass from Iniesta saw Marc Montoya set up Fabregas to score a third after 63 minutes and the former Arsenal captain then headed a fourth goal in off the post in the 79th.
A Betis penalty at the end from Jorge Molina was little more than a consolation.
"These games are important for me to be able to prove myself," Fabregas, who is to have tests on a sore knee ligament, told Spanish broadcaster Canal Plus.
"I had a good game against Celta Vigo and then was out of the team for the best part of two games and this upsets you. I want to make sure it doesn't happen again."
Diego Simeone's Atletico side were on course for a victory after a Villarreal own-goal in the second minute.
Juanfran's cross forced Mario to head into his own net under pressure from Koke, and the visitors then put in a typically abrasive performance in an intense tussle.
Villarreal were finally rewarded for their endeavour when Jeremy Perbet got to the line and crossed to the near post where striker Ike Uche slid in with Juanfran, and the Atletico defender poked the ball over the line in the 79th.
"It's an important point against a direct rival," Simeone told a news conference.
"The players are playing a lot of games in succession and perhaps it showed at times. I congratulate them. They are putting in a huge effort."
Real Madrid sit third with 31 points after Cristiano Ronaldo scored a hat-trick in their 5-1 home rout of Real Sociedad on Saturday. Promoted Villarreal are fourth with 24.
There were whistles at the Mestalla where Miroslav Djukic's Valencia had to come from behind to draw 2-2 against his former club Real Valladolid with a 75th-minute strike from substitute Sofiane Feghouli.
The hosts got off to a woeful start, Ever Banega hoofing a penalty over the bar after only five minutes, and they then conceded a ninth-minute Javi Guerra header.
Colombia striker Dorlan Pabon's long-range effort put Valencia level in the 29th, and after Valladolid notched a second through Gilberto Garcia just after the restart, Feghouli rescued a point for Djukic's inconsistent side.
Sevilla ended a run of 22 consecutive away games without a win in La Liga when they triumphed 3-1 at Espanyol.
The Andalusians last won on the road in the league in September 2012, beating Deportivo La Coruna 2-0, and coach Unai Emery was feeling the heat after five games without a win in all competitions.
Quick goals from Federico Fazio and Vitolo gave Sevilla the advantage and Carlos Bacca made sure of the points with an impressive third in the 58th minute, running from the halfway line to fire home. (Reporting by Mark Elkington, editing by Justin Palmer and Ken Ferris)