The Pittodrie team got back to winning ways in style thanks to striker Niall McGinn's second-half hat-trick which proved far too much for Barry Smith's lowly Dark Blues team.
McGinn struck three times after the break to ensure the Reds rounded off 2012 on a positive note and Brown, who has lost defender Andrew Considine to a broken leg in the first half, wants to see them take that kind of form into the New Year.
He said: "We're all really pleased with the win, not just the end result but the overall performance as well.
"Our results had not been the best of late so we knew there was some work to do to get back doing what we know we can do.
"Hopefully this is the start of something where we can go on a wee run over the next few games.
"The lads are buzzing and we had some very good individual displays as well as working very hard together as a team.
"Dundee is never an easy place to come to and they are fighting at the bottom so we can take a lot of heart from what we've achieved here."
Meanwhile, McGinn insists he has not set himself any scoring targets after taking his tally for the season so far to 14 with goals in the 46th, 68th and 88th minutes.
The Northern Ireland international said: "I'm delighted obviously with the goals.
"I've got a few this season but it's not about me.
"I couldn't do it without the help of my team-mates who set them up for me.
"In saying that, there are no real targets.
"I just want to carry on playing as well as I can and I'm sure there will be more chances along the way. It will then be up to me to try and take them for the good of the team."
Dundee manager Barry Smith has told his players not to dwell on their latest defeat which leaves them nine points adrift at the foot of the SPL as they bid to survive in the top-flight.
Smith, whose side travel to face St Johnstone on Wednesday, said: "We just have to get it out our system as quickly as possible.
"That's why it's good to have another game to look forward to so soon.
"We'll pick ourselves up and get on with it.
"We won't feel sorry for ourselves because there's a lot of points to be played for between now and the end of the season.
"The lads are hurting but they give everything which is what we want at this club."
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