Neymar opened the scoring midway through the first half from a pass by Dani Alves, who also set up Suarez for the defending champions’ second just before halftime.
Neymar took his competition-high tally to 14 goals soon after the interval as he extended his scoring streak to four straight league matches.
With the result beyond doubt, Neymar and Suarez went to pains to try and set up their strike partner Messi, who went close three times and struck the upright before he got his goal to round off the rout in stoppage time. He has scored three times in three appearances since returning from a two-month injury layoff.
“It comes naturally for them. They look out for one another and aren’t happy unless all three score,” Barcelona coach Luis Enrique said.
Suarez, meanwhile, has scored in six consecutive rounds, and remained second in the league with 12 goals.
Second-place Atletico Madrid remained four points behind Barcelona after edging Espanyol 1-0 in the capital.
Antoine Griezmann scored his third goal in his last two games early in the match, and Espanyol never threatened to rally.
Atletico lost midfielder Tiago Mendes in the first half when he was carried off and taken to hospital for tests on his right leg after he injured it kicking Espanyol’s Marco Asensio in the back.
Barcelona was unstoppable for the third time in eight days after humbling Real Madrid 4-0 in last weekend’s clasico and obliterating Roma 6-1 in the Champions League.
Luis Enrique’s team has won nine of its last 10 games to go with one draw in the Copa del Rey that it played with reserve players.
When asked if his team provoked fear among its opponents, Luis Enrique said: “That’s a question for our rivals.”
Coached by former Barcelona player and assistant manager Eusebio Sacristan, Sociedad tried to disrupt Barcelona’s possession by pressuring far up the pitch.
The strategy, however, only left Neymar, Suarez and Messi with more room to romp.
Andres Iniesta headed Suarez’s pass off the post early on.
Barcelona kept arriving with ease on both flanks and Dani Alves was played through by Messi to square the ball for Neymar, who beat his marker and stabbed Barcelona’s first goal into the top of the net.
Dani Alves was again the assist-giver for Suarez when Iniesta sent him clear on the right side with a long ball. Suarez made a tough strike look easy as he drove in the cross with an acrobatic kick.
Barcelona’s third came from an incursion by left back Jeremy Mathieu, who ran onto Iniesta’s pass and crossed for the unmarked Neymar to tap in.
Messi’s goal was just as easy when Neymar spotted him in injury time.
Sociedad, in its second match since Sacristan replaced David Moyes, remained two points above the relegation zone.
Later, bottom side Malaga played Granada, Deportivo La Coruna visited Las Palmas, and Celta Vigo faced Sporting Gijon.