Knowing a win would catapult either side into the finals-bound spots, the clash at Brisbane's Spencer Park on Friday night was crucial with just two rounds remaining.
The Roar turned up the heat, with Brown breaking the deadlock after a tense first half, before going on a scoring rampage to help the home side emerge victorious.
Earlier, Wellington jumped to second spot after coming back against cellar-dwellers Sydney FC for a 3-1 win at Leichhardt Oval.
Victory cements the Phoenix's spot inside the top six. They have never made finals, but now sit just three points behind ladder leaders Melbourne City with three games left.
It wasn't an easy victory after Sydney young gun Caley Tallon-Henniker curled the ball into the bottom left corner in the third minute.
But Wellington flicked a switch first through Brooke Nunn, who unleashed a classy through ball for Pia Vlok to score.
Defender Marisa van der Meer scored for the first time this year when she headed a lofted cross from Manaia Elliott into the roof of the net in the 64th minute.
Nunn then iced the result when she converted a switch pass from Vlok.
Despite a lengthy injury list, Brisbane overcame Newcastle to jump into fifth place and go two points clear of the seventh-placed Perth.
The result will come as a welcome relief after the wheels looked to be falling off the Roar's season, having lost their previous four matches.
Brown stepped up to score her club's first goal in 426 minutes when her head found a superb ball from Ashlyn Miller.
Five minutes later she made the most of Newcastle goalkeeper Georgia Ritchie's lack of concentration, finding the net again when she whacked the ball and it took a deflection into the bottom right corner.
Midfielder Bente Jansen then added a fourth for Brisbane, but Newcastle grabbed two late consolation goals through defender Natasha Prior and midfielder Sophie Hoban.
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