Barca are level on 22 points with Real Madrid after eight games but have a better goal difference before the pair face each other next Sunday in El Clasico at the Santiago Bernabeu.
It was the seventh consecutive league win for Barcelona, who started well with Gavi and Raphinha running the channels and creating several scoring opportunities.
Celta's Argentine goalkeeper Agustin Marchesin made an incredible save in the 10th minute with the tip of his left hand to keep out a brilliant long-range shot from Raphinha.
However, he was beaten seven minutes later by Pedri's close-range strike from a rebound after capitalising on an error by defender Unai Nunez who tried to clear Gavi's cross.
Teenage sensation Pedri was again on hand to find the net, having scored eight goals from 16 shots on target in LaLiga, scoring with each of his last four.
Celta looked much better after the break, taking control of the ball and creating several chances, but were denied by the brilliance of goalkeeper Marc-Andre ter Stegen.
The German international extended his clean-sheet streak in LaLiga to six games, while he has not conceded a goal in seven of Barca's eight league games this season.
"We need to be self-critical today, we have to be much better than we were today," Barca coach Xavi Hernandez said.
"Our team played well in the first 30 minutes, could have scored more goals, but they were better than us in the second half."
After Celta's good start to the first part of the season, they have lost three of their last four league games and are 11th on 10 points, four above the relegation zone.
Real Betis held on to a 0-0 draw at Valladolid despite playing more than an hour with a man down as defender Germán Pezzella was sent off in the 35th.
The result dropped Manuel Pellegrini's team to fifth place with 16 points from eight matches.
Valladolid, coming off their second win of the season, were in 13th place.
Joselu scored twice in the second half but Espanyol were held by 19th-place Cádiz to a 2-2 draw, extending their winless streak to four matches.
The result left the Barcelona club just outside the relegation zone.
Cádiz are unbeaten in three games after losing their first five.
