Lionel Messi was forced off in the first half - the third time he has been hit by hamstring problems this season - with the club confirming on their Twitter feed during the match that he would undergo a scan on Monday.
Neymar and Pedro scored in the first half before Fabregas added a brace in the second period to seal a win that moves Barca three points clear at the top of the Primera Division table after Atletico Madrid were held to a 1-1 draw by Villarreal.
Jorge Molina scored a 90th-minute penalty for Betis, who remain rock bottom to keep the pressure on coach Pepe Mel.
Atletico dropped points for just the second time this season at fourth-placed Villarreal.
A second-minute Mario Gaspar own goal gave the capital club the lead, but they duly handed it back when Juanfran turned the ball into the wrong goal 11 minutes from the end.
Sevilla halted a two-match losing streak with an impressive 3-1 victory at 10-man Espanyol.
Los Rojiblancos made an ideal start at the Estadi Cornella-El Prat as Federico Fazio and Machin Vitolo put them two goals to the good inside the first 10 minutes.
The home side's captain Sergio Garcia pulled one back midway through the first half but Carlos Bacca restored Sevilla's two-goal lead and it proved decisive.
Valencia twice came from behind to earn a 2-2 draw at home to Real Valladolid, but will consider it two points lost after dominating possession and missing an early penalty.
Ever Banega skied a spot-kick after five minutes and Javier Guerra then gave the visitors the lead against the run of play.
Dorlan Pabon equalised for Valencia just before the half-hour mark but Gilberto Alcaraz put Valladolid ahead again early in the second half. Sophiane Feghouli equalised on 76 minutes.