"I know the starting 11 that my coach has in his head and that I am not in it," Fabregas said. "I will work as much as I can to erase any doubts."
Barcelona said Messi and Fabregas would undergo tests on Monday to determine the extent of their injuries.
Goalkeeper Victor Valdes made two superb saves to deny Jorge Molina before Fabregas set up Neymar for Barcelona's 35th-minute opener.
Pedro Rodriguez made it 2-0 two minutes later with a solo effort that left Betis' defense in tatters, and Fabregas finished off the scoring for Barcelona in the 63rd and the 79th.
Barcelona's 12th win in 13 rounds kept it undefeated and lifted it three points clear of second-place Atletico after it was held to a 1-1 draw at Villarreal earlier.
Messi, who appeared to be back to his old self after scoring a double on Wednesday against AC Milan in the Champions League, hurt a muscle in his left thigh while sprinting and was replaced by Andres Iniesta.
"No doubt we will have to talk to Leo so that this third injury doesn't worry him and affect him mentally," Barcelona coach Gerardo Martino said.
Last-place Betis had already tested Valdes by the time Messi went off, but the Spain goalie continued his excellent season by denying Molina one-one-one, and moments later leaping to turn away the striker's header at the far post.
Having regrouped after losing Messi, Alex Song met Fabregas' run with a weighted pass that left him free to cross for the unmarked Neymar, who scored his fourth league goal of the season.
Pedro then raced onto a high ball in midfield, knocked it beyond Betis' last line of defense, and collected it before looping a shot beyond goalkeeper Guillermo Sara.
Betis' Joan Verdu went close and Jose "Nono" Delgado hit the woodwork as the hosts tried to react after halftime. But coach Pepe Mel's insistence on pushing his defensive line up the pitch proved fatal.
Neymar had threatened twice on the break before Iniesta lobbed the ball wide to Martin Montoya, who had three Barcelona players to cross to in the area against one Betis defender.
Montoya chose Fabregas to tap in his first goal before the former Arsenal midfielder nodded Dani Alves' pass off the turf and the upright before it trickled over the goalline. Three minutes later, Fabregas left the match.
"We tried to make long passes behind their defense to look for the open spaces they were leaving, and I think we took full advantage of them," said Pedro.
Molina finally beat Valdes from the penalty spot for Betis' consolation goal in stoppage time after Dani Alves fouled Javier Matilla in the box.
Atletico went ahead just two minutes into the match at El Madrigal Stadium when Juanfran Torres broke free on the right flank and swung in a cross that defender Mario Perez turned into his own net while trying to fend off Jorge "Koke" Resurreccion.
Atletico held Villarreal's passing attack in check until coach Marcelino Garcia sent on striker Jeremy Perbet.
Five minutes later Perbet provided the missing spark when he collected the ball from a throw-in, dribbled into the area and provided a square pass that Juanfran ended up poking into his own goal while jostling with Villarreal's Ikechukwu Uche.
Villarreal remained in fourth place, but seven points behind Real Madrid in third.
Earlier, Sevilla beat Espanyol 3-1 to end a 22-game winless run away from home in the league, while Valencia was held to a 2-2 draw by Valladolid to remain without a victory in its last three home games.
Sevilla got the much-needed victory thanks to goals from Federico Fazio, Vitolo Machin, and Carlos Bacca. Sevilla hadn't won away in the league since Sept. 24, 2012.
Espanyol finished with 10 men when Victor Sanchez received his second booking with five minutes to play.
After Valencia's Ever Banega missed a penalty, Javi Guerra headed Valladolid in front in the ninth minute before Dorlan Pabon leveled in the 29th.
Gilberto "Alcatraz" Garcia, who had set up Guerra's opener, drilled in Valladolid's second goal in the 50th, only for Sofiane Feghouli to guide home a cross by Sergio Canales in the 76th to share the points.
