Goals from Darren Mackie, Chris Clark and Ryan Jack helped the Dons end a run of three straight defeats against a disappointing United, who had gone into the match on the back of a six-game winning run.
Brown admitted he will now have a tough task choosing his starting line-up for next week's Hampden showdown.
He said: "I was pleased with the whole team and I won't single anyone out. The players were up for the fixture and it gives us a major selection problem for next week, which is a very good problem to have.
"There's no point in winning that match and then going on and losing next week. If you had to choose you would do it the other way round, but if we can do both that would be ideal."