Lionel Messi had looked far from his best in Barca's Super Cup victory over Atletico Madrid in midweek, but looked more like his old self as he put Barca 2-0 up inside 39 minutes and was then brilliantly set up by Neymar to complete his hat-trick.
However, Valencia were amazingly back in the game by half-time as Helder Postiga struck twice in first-half stoppage time.
Barca then passed up a host of chances to put the game to bed in the second-half and were nearly punished when Jonas struck the post four minutes from time.
Neymar had already had a goal ruled out for offside when Cesc Fabregas sprung Valencia's high line with a fine through ball on 10 minutes and Messi evaded challenge from Adil Rami and Diego Alves to bundle home from close range.
Victor Valdes was then forced into a fine save to deny Dorlan Pabon levelling on his debut for Los Che.
But just when it appeared Valencia were in control of the game, Barca struck twice in two minutes.
Firstly, Sergio Busquets robbed the ball in midfield to allow Fabregas to set Messi free again to roll into the far corner.
And then a wonderful piece of individual skill from Neymar teed-up the Argentine to side foot home his 23rd hat-trick for the Catalans.
Valencia responded wonderfully though and were back in the game before half-time thanks to Postiga's double.
The Portuguese firstly produced a stunning overhead kick to turn Joao Pereira's cross into the top corner.
And moments later the former Spurs man rose highest to flick home Ever Banega's corner.
The frantic pace continued after the break as Messi forced Alves into a stunning save from the edge of the area before Pedro somehow managed to head wide from Andres Iniesta's cross from point-blank range.
Messi was next to let Valencia off the hook as he unbelievably pulled his shot wide after more great work from Neymar and Jordi Alba down the left and then fired straight at Alves when clean through on goal.
And the champions were nearly made to pay for their profligacy as Jonas' curling effort from the edge of the area was brilliantly turned onto the post by Valdes.
Earlier, Real Madrid continued their unblemished start under new manager Carlo Ancelotti with a 3-1 win over Athletic Bilbao at the Santaigo Bernabeu.
Isco was the hero for the hosts as he opened the scoring with a neat finish from Karim Benzema's lofted pass.
Cristiano Ronaldo then headed in his first goal of the season from Angel Di Maria's free-kick and Isco's deflected effort made the game safe for Carlo Ancelotti's men.
Ibai Gomez pulled a late goal back for Athletic, but it mattered little as Madrid ensured their best start to the league campaign in four years.
"The fans have enjoyed today. It was our best performance of the season," Luka Modric told reporters after he too shined in Madrid's new-look midfield.
"Every game we play we are improving. Last season I didn't have a pre-season and it is very difficult to get up to speed.
"This season I have been able to start from scratch with my teammates."
Atletico Madrid also maintained their perfect start to the campaign with a 2-1 win away at Real Sociedad.
David Villa and Koke scored either side of half-time to put Diego Simeone's men in charge.
However, the visitors were thankful to Thibaut Courtois for the three points as the Belgian produced two stunning saves after Xabi Preito had reduced Sociedad's arrears 22 minutes from time.