Suarez struck in the 50th and 71st minutes, his first a delightful chip from just inside the area, after laying on Paulinho six minutes before the break to start the comeback from first-half goals from Sociedad's Willian Jose and Juanmi.
A stunning Lionel Messi free-kick five minutes from time completed the comeback, which puts Ernesto Valverde's side on 51 points, well ahead of second-placed Atletico Madrid, 1-0 winners at Eibar on Saturday.
The win also moves Barca a full 19 points in front of arch-rivals Real Madrid, who are languishing in fourth and closer on points to the relegation zone than leaders Barca after Saturday's 1-0 home defeat by Villarreal.
Real's embarrassment allowed third-placed Valencia to move eight points clear of Zinedine Zidane's side with a 2-1 win at third-from-bottom Deportivo La Coruna on Saturday, which came thanks to goals from Goncalo Guedes and Rodrigo.
Jose gave the hosts a shock lead after just 11 minutes when he headed home Xabi Prieto's superb cross, and a shambolic looking Barca were deservedly two down 23 minutes later.
Juanmi burst through the away side's distracted backline to meet Sergio Canales' excellent through ball, and the Spaniard saw his shot deflected off Sergi Roberto and creep inside Marc-Andre Ter Stegen's near post.
Suarez burst into life as the first half came to a close and gave the Catalans hope with a fine low cross that Paulinho just had to guide home to pull a goal back.
Rulli's long clearance was fired back with a powerful shot by Thomas Vermaelen that found Suarez clean through on and ready to crash home Barca's third.
Messi's free-kick, a dipping curler that any goalkeeper would have struggled to save, was the icing on the cake for Barca and the Argentine, who overtook Gerd Muller to become the top scorer in the history of Europe's top five leagues with his 366th La Liga strike.
================
Real coach Zidane was given some respite from the fierce criticism he received following Villarreal's first ever win at the Bernabeu, as Sevilla missed the chance to draw level on points in the race for Champions League qualification when they lost 1-0 at lowly Alaves on Sunday.
Manu Garcia's 52nd-minute strike pulled Alaves out of the relegation zone and left Sevilla sixth on 29 points, three behind fourth-placed Real.
The defeat for Sevilla extends Vincenzo Montella's losing start in La Liga, with the Italian guiding his new club to two straight league losses since replacing cancer-stricken Eduardo Berizzo, following last week's 5-3 home Seville derby loss to Betis.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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