Barca missed a string of chances against a dogged Sevilla at Camp Nou before the 19-year-old Pedri settled the contest with a moment of magic, dancing his way into space on the edge of the area before firing into the corner.
Victory continues Barcelona's recent surge as they backed up their 4-0 thrashing of Real Madrid before the international break with a convincing win against the team who have been Madrid's chief title challengers all season.
Madrid edged past Celta Vigo on Saturday to calm suggestions their Clasico nightmare could even prompt a late collapse and let Barca back into the race.
A 12-point advantage means that is surely impossible now but Barcelona are in the driving seat to finish second, which would be a remarkable achievement for a team that only a few months ago had serious
concerns about missing out on the top four. When Xavi took over in November, they lay ninth.
The last time the Catalans were second in La Liga after a complete round of fixtures was May 10 last year, three matches before the end of last season.
"We're second but nothing is done," Xavi said. "While it's mathematically possible to fight for La Liga, we will keep fighting."
Ousmane Dembele delivered another excellent to display to enhance the growing the sense that the Frenchman might yet stay in the summer, even if the club remain pessimistic.
Pedri, though, was the star of the show, a stunning performance in midfield rounded off with a masterful goal that will only further the reputation of one of the world's most exciting young talents.
"I encourage him to shoot," said Xavi. "He always thinks to pass, he's a passer, it's something that happened to me as well. But today he scored a great goal.
"When I say he's an elite player, it's because there is hardly anyone that understands our style as well as him."
- Sevilla slump continues -
Sevilla, meanwhile, continue to fizzle, have drawn seven out of their previous nine games before this defeat made it two wins from 10.
Add the surprise exit in the Europa League at the hands of West Ham and Julen Lopetegui's side are in danger of enduring a miserable end to what looked a promising season.
Barcelona were the more assertive team in the first half but it was only in the last 10 minutes that Sevilla were made to feel uncomfortable as a flurry of chances went begging.
A sumptuous Pedri pass released Dembele out on the right but his attempted cut-back was intercepted.
Then Pedri picked out Dembele again, this time with a clipped cross into the area and while Dembele nodded smartly across the six-yard box, neither Ferran Torres nor Pierre-Emerick Aubameyang could convert.
Aubameyang was slipped through by Dembele, only to see his finish clawed away by Bono as Sevilla survived, the score goalless at the break.
The pattern, though, was set and while Sevilla were less frantic after the restart, Barcelona remained in charge. Dembele squared for Torres, whose finish was pushed over. Jordi Alba cut back for Torres but this time he curled wide.
A sloppy Dembele pass gave Ivan Rakitic a chance at a free-kick but he floated the shot just over, allowing the Barca assault to continue, Gerard Pique driving wide and then heading the resulting corner against the crossbar. Sergio Busquets volleyed the rebound over.
When Dembele missed at the back post with 20 minutes left, it felt like Barca would never score, until Pedri intervened.
Dembele's pull-back found the teenager on the edge of the area but Rakitic and Diego Carlos were rushing out to him.
He floored Rakitic with one dummy and then left Diego Carlos for dead with a second, firing through the sprawling bodies around him and into the bottom corner.