Rory Fallon, scorer of both goals in the Scottish Cup quarter-final win at Fir Park last season, netted the 51st-minute opener and Joe Shaughnessy tapped in 10 minutes later, as the Dons won the fourth-round replay 2-1 to set up a fifth-round clash with Hibernian at Easter Road.
Motherwell, the 2011 runners-up, had lost just once in 13 prior games against Aberdeen, but Brown's side have turned the momentum round since he and assistant Archie Knox moved from Fir Park to Pittodrie two years ago.
"We've now managed to turn it round against Motherwell," Brown said.
"That's four games and it's two wins and two draws for us.
"Between the first and the second goal we had three really good chances and (Motherwell goalkeeper Darren) Randolph had two saves in the game which were world class."
Hibs beat the Dons in last season's semi-final, but Brown's men will be hoping to repeat last month's 1-0 Clydesdale Bank Premier League at Easter Road to progress.
Brown added: "It's another testing fixture. We've got to rise to the occasion again.
"We've done very, very well away from home, so an away game is not a disadvantage to us."