United, looking to move into outright top spot, were on the front foot at Spencer Park thanks to Sofia Christopherson's 13th-minute goal on Friday night.
But from there it was all the Roar, with Daisy Brown levelling the scores in the 45th minute, before substitute Freier put the home side in front in the 66th minute.
Bente Jansen put on the finishing touches in the 89th minute, with Canberra's star Matildas striker Michelle Heyman resigned to simply watching.
Brisbane (18 points) soar from ninth to fourth ahead of the weekend's clashes, now on a five-game undefeated streak.
Canberra are also on 18 points and remain second after losing their past two matches, having suffered a 2-0 loss to Wellington Phoenix in their previous game.
But United could slip out of the top four, with third-placed Central Coast also on the same number of points and Adelaide fifth on 17 points.
It was a goalkeeping blunder by Roar shot-stopper Chloe Lincoln that opened the door for Canberra in the first half.
With two Roar defenders streaming down the right wing, three-cap Matildas goalkeeper Lincoln instead gave the ball straight to Christopherson.
Named in Canberra's starting line-up for the first time, Christopherson had gone for home from outside the box.
But Canberra couldn't defend their lead to halftime, after Brisbane midfielder Ashlyn Miller broke away in the 45th minute.
Miller brilliantly outworked a challenge from Canberra opponent Elizabeth Anton to set up Brown's goal.
Starting the better side after the break, Brisbane found their spark when substitute Freier joined the fray in the 57th minute.Â
Freier easily won a duel with Canberra's Hayley Taylor-Young down the right wing to score less than 10 minutes after coming off the bench.
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