Barca's next game is in the Santiago Bernabeu on November 21 against arch-rival Real Madrid, who later slumped to a 3-2 defeat at Sevilla to fall three points behind the Catalan giants.
Sergio Ramos put Real ahead with a overhead volley but damaged his suspect left shoulder in scoring, being substituted within minutes.
Ciro Immobile equalized for Seville just before the break, scoring from a tight angle after a corner.
Real, suffering its first defeat of the season, conceded further goals from Ever Banega and Fernando Llorente after the break.
A 90th minute reply from James Rodriguez was not enough to rescue Los Blancos.
European champion Barcelona has been without its star player Lionel Messi for the past six weeks, but Neymar and Suarez have stepped into the breach by scoring all 17 of its league goals since his injury layoff.
Their incredible record was maintained after a scoreless first half in the Nou Camp, the on-form Neymar converting after a Sergio Busquets through ball.
Suarez stepped up to take the penalty for the second after Munir El Haddadi had been brought down by Jaume Costa.
Neymar might have taken the spot kick and Suarez returned the favor by supplying the pass from the Brazilian conjured up a magical third, flipping it over a defender
and volleying home. He has scored a league leading 11 goals and 13 in all competitions.
"We are talking about a unique player, special. We have to look at his work." said Barcelona boss Luis Enrique as he reflected on a vital win.
"That the team is growing and improving in key aspects of the game is obvious," he told the official Barcelona website.
"Right now Neymar is the most dominating striker in the league," said Villarreal head coach Marcelino Garcia Toral.
Earlier, Athletic Bilbao secured its fifth straight win in all competitions, set on its way by a wonder goal from Inaki Williams in a 3-1 victory over Espanyol.
The young striker converted with a spectacular volley after flicking the ball over Enzo Roco before unleashing a spectacular volley into the top corner.
Hernan Perez leveled for the visitors just after halftime but Raul Garcia headed home the winner for Bilbao midway through the second half.
Atletico Madrid took closer order in third place, four points adrift of Barcelona, with a 1-0 home win over Sporting Gijon.
Man City tops EPL
In the English Premier League, Manchester City stayed top of the standings on goal difference from Arsenal on a Sunday afternoon which saw a thrilling 1-1 draw in the North London derby and the first defeat for Jurgen Klopp at Liverpool.
City was held to a goalless draw at bottom club Aston Villa where Remi Garde took charge for the first time, but Arsenal missed the chance to go above them after a 1-1 home draw against Tottenham Hotspur.
Harry Kane put Spurs, unbeaten in the EPL since the first game of the season, deservedly in front with a first half opener as the visitors had the better of a closely fought match.
Arsenal saw Olivier Giroud waste a series of headed opportunities in the second half but Tottenham again made the better openings with Kane and Christian Eriksen going close.
Substitute Kieran Gibbs proved an unlikely savior for the hosts as he connected with a Mesut Ozil pass at the far post and it was Arsenal who finished on the front foot.
Liverpool trailed at Anfield to a Yannick Bolasie opener for Crystal Palace in the 21st minute but looked to have regained the initiative when Phlippe Coutinho leveled just before halftime.
But it was Palace who took the three points through Scott Dann's winner with eight minutes to go, sealing a third straight victory over the Merseyside giants after completing a league double last season.