Dortmund started the calendar year nine points adrift of Bayern but followed last week’s dramatic 3-2 win at Eintracht Frankfurt with a routine home victory over a potentially tricky Freiburg.
Christian Streich’s fourth-placed side had beaten Dortmund in their home fixture but succumbed easily.
Meunier twice headed in from Julian Brandt corners for his first goals of the season and regular scorer Haaland ended a mini drought – of two games – with the third before half-time.
Freiburg substitute Ermedin Demirovic cut the deficit on the hour but Haaland added a fourth with 15 minutes remaining to remove any doubt and a late strike from Mahmoud Dahoud completed the rout.
Bayern will look to restore their six-point lead, and bounce back from last week’s home defeat to Borussia Moechengladbach, away to Cologne on Saturday.