Barcelona have now won all four of their league matches, establishing themselves as the only team in the Spanish top flight yet to drop a point.
Yamal opened the scoring after just five minutes, showing excellent composure to lift the ball over Valencia goalkeeper Stole Dimitrievski after being found by a clever pass from Fermin Lopez.
The teenager appeared to have scored again moments later, but his effort was ruled out for offside following a VAR review.
Barcelona dominated possession throughout the opening stages and were in complete control. Valencia struggled to create opportunities, with David Otorbi missing their first real chance after more than 15 minutes.
Barcelona immediately responded at the other end, with Fermin Lopez doubling their advantage by driving a left-footed shot into the bottom corner.
Valencia briefly threatened when Arnaut Danjuma forced Joan Garcia into action after a mistake from Rodri, but Barcelona remained the more dangerous side.
Fermin came close to adding another before the break when he created space brilliantly inside the box, only to see his effort strike the woodwork.
The second half followed the same pattern, with Barcelona controlling the game and Valencia unable to find a way back into the contest.
Raphinha made it 3-0 when he finished from close range, before Rodri came close to reducing the deficit for Valencia when his powerful header struck the crossbar.
Barcelona continued to play with the confidence of a team already in complete control, and their substitutes made little difference to the pattern of the match.
Pedri added a fourth with just over 10 minutes remaining, combining with Dani Olmo before calmly finishing the move.
Yamal then completed the rout soon afterwards, scoring his second of the night after another assist from Olmo.
The result leaves Valencia with their worst four-game start to a season in the last decade, while Barcelona continue to dominate this fixture. It was their 11th victory in the last 14 meetings with Valencia.