Since Vilanova stepped up from assistant coach at the end of last term to replace Guardiola, who is taking a well-earned rest from the game, Barca have won 13 and drawn one of their opening 14 league matches and top the standings on 40 points.
Saturday's crushing 5-1 victory at home to Athletic Bilbao meant they eclipsed the record of 39 points set by Real Madrid in the first 14 games of the 1961-62 campaign.
They lead their nearest challengers Atletico Madrid, who lost 2-0 at third-placed Real on Saturday, by six points.
The best start managed by Guardiola, who led the club to 14 trophies during his four years in charge, was 37 points from 14 games in the 2010-11 season.
"Those four years will never be repeated for everything that was achieved, for the titles, the way we played," Vilanova told a news conference.
"I feel proud because I was also part of that and I have only been in charge for a very short time," he added.
"I am very happy to set the record of wins but I am more happy about the performance of the players, who knew how to control the game.
"Even though we were winning 5-1 we kept pressuring with the aim of scoring more goals.
"Playing like that for sure we'll be strong, we'll win a lot of matches and we'll be up there competing for titles."
With an 11-point lead over arch rivals Real, who suffered a poor start to their title defence, Barca are well placed to win a fourth La Liga title in five years and are also through to the last 16 of the Champions League as group winners.
The only points they have dropped this season came in October's "Clasico", a 2-2 draw with Real at the Nou Camp.
