Neither side were able to truly take control of the match and find a breakthrough despite both the Roar and City having their fair share of chances on goal.
With two rounds to play, Brisbane hold a three point lead over Sydney at the top of the W-League ladder while Melbourne cling onto fourth spot by a mere point ahead of Canberra who still have a game in hand.
It wasn't until the 20th minute for the first real chance of the match when City's Rhali Dobson fired across the face of goal after a precision pass from Jess Fishlock.
As City pushed forward, Kyah Simon had a chance tipped over the bar while Steph Catley was also denied by Brisbane shot stopper Mackenzie Arnold.
Brisbane's best chance fell to Hayley Raso who had her powerful shot from the edge of the box saved by a diving Lydia Williams.
Brisbane will be secure a first place finish next week when they travel to Adelaide to take on Adelaide United, while Melbourne City have a bye.
