The Premier League curtain raiser at Turf Moor featured a side managed by Manchester City old boy Vincent Kompany, who came face-to-face with Pep Guardiola.
In the end, it was the champions who taught the hosts a painful football lesson with Haaland grabbing a brace and Champions League hero Rodri scoring the other.
Burnley finished the game with ten men after Anass Zaroury was sent off late on.
Speaking after the game, Guardiola said: "The first game of the season, away, against a newly promoted team with this passion and love is always so complicated and tricky.
"Apart from 10 or 15 minutes when we gave the ball away, the team again showed the heart and passion that they still want to do it.
"Vinny changed completely the way they play. Sean Dyche was magnificent for this club. It is not an easy place to come and a lot of games here, teams are going to suffer and that is why I am really pleased. Against high pressing, man-to-man teams Erling is an incredible weapon in behind.
Man City will turn their attention towards the UEFA Super Cup against Sevilla on Wednesday.
