Mr Brownlee, accompanied by six officials, was on his way to a Parliamentary committee hearing that started at 10.30am when the Beehive lift they were in stopped dead.
"We got in and then had trouble getting out that's about it. I was with my close friends who are now much closer," Mr Brownlee told reporters.
There were no other MPs he said: "I said, people I am close to".
"We got talking about things, life stories, that type of thing, one or two started writing their last will and testament.
"I was trying to work out whether we could pick a hole in the wall to perhaps get a cup of tea through, it seemed to pass pretty quickly."
Mr Brownlee offered to speak to the committee by phone but it declined, wanting to see him in person. When he finally arrived he was welcomed into the room by loud applause.
It was not immediately clear what caused the problem. The lift has a weight carrying maximum of 545kg but doors do not close when that is exceeded.
