Ronald Koeman had called on his players to produce a performance befitting the former Barca and Argentina star, who died this week.
They duly delivered, Griezmann scoring the pick of the goals in a fine performance against a side who won 2-1 at this ground in July.
The breakthrough eventually came in scrappy fashion. Messi's pass split the defence, Jordi Alba found Coutinho, Sergio Herrera saved his shot and Braithwaite's rebound, but the latter managed to bundle the ball over the line with Messi's help.
Ante Budimir turned past Marc-Andre ter Stegen after a brilliant double save by the keeper, but the goal was correctly ruled out for offside against Oier Sanjurjo.
Barca doubled their lead just two minutes later, Griezmann walloping a volley past the motionless Herrera after Alba's cross had been cleared to the edge of the box.
Griezmann turned provider 11 minutes into the second half, teeing up Coutinho for a tap-in after good work from Braithwaite to win back possession in the Osasuna half.
A good outing for the Catalans was soured when they suffered another defensive injury, Clement Lenglet unable to continue after apparently taking damage to his ankle.
Roberto Torres rattled the post before Ousmane Dembele had a goal ruled out for offside, but Messi soon made it 4-0 with a fierce strike from the edge of the box, the Argentine then removing his Barca shirt to reveal a Newell's Old Boys jersey emblazoned with the number 10.
Barca edge closer to leaders
Barca's victory moves them into seventh place, three points behind champions Real Madrid in fourth, with a game in hand.
They can take some confidence into coming league matches with Cadiz and Levante before the meeting with leaders Real Sociedad on December 16.
Osasuna are 15th, three points above the relegation places.
