South Africa will win Pool B if they beat USA on Wednesday as expected and the second qualifying spot will be decided by Scotland's game against Samoa at St James' Park, with Vern Cotter's men currently two points ahead of Japan who face USA on Sunday.
The Scots have only had four and six days respectively between their previous group matches but with a full week to prepare, Brown believes his side will be in a much stronger position heading into the crucial clash with Samoa.
"The big thing for us is it's the first time we've had a full week between games," Brown told the Glasgow Evening Times.
"We had four days between Japan and USA, six days until South Africa, so it's the first time we can go through a proper post-match recovery and training. We can have a couple more training sessions this week and work more on shape and our set piece and how we want to approach the game.
"Our destiny is still in our own hands. We can still qualify for the quarter-finals. We have to win next weekend and then we've got a quarter-final.
"We approach it as we have done all the other games, knowing that we have to go out there and play well. We have to win, and if we win we're in the quarter-finals."
Scotland left themselves with a mountain to climb against South Africa at the weekend as they were already 20-3 down by half-time.
So Brown, who came on as a replacement in the GUINNESS PRO12 final in May, has stressed the importance of starting well against Samoa as the consequence could be they join neighbours England in exiting the World Cup at the pool stages.
He added: "The big thing for us is just believing from the first minute that if we go out and we keep hold of the ball and we impose ourselves in attack and defence, then we can score lots of points, we can put teams under pressure.
"We let ourselves down a little bit in the first half [against South Africa]. Then all we said to ourselves at half-time was we need to pride ourselves on our physicality, we need to front up and keep the ball.
"So I think our second-half performance was much better, but we just lost that physicality battle, especially in the first half. It was probably the most physical game I've had."
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