Bernoulli did not come down the chimney

As promised, I am here to make amends for an incorrect paragraph on the Bernoulli Effect. So here goes with another try. If the wind blows past a door - parallel to it - the air pressure on that side of the door is lower than on the other side and so the door would swing out, not in. If, on the other hand, the wind blows straight into the door, obviously the door would swing in, as was the case during the storm. So far so good.

Now why did the wind blow down the chimney? If the wind was blowing across the top of the chimney and not down into it, the air pressure at the top would be lower than the still air within and air would push up the chimney, not rush into the house.  Sometime during the storm, in my house, the air pressure at the top of the chimney was higher than within and woosh, the air rushed in, dust and all. If anyone out there has a better explanation of why this happened, please inform.