The Dons broke their home goalscoring duck last week when Gavin Rae headed the opener against Motherwell but they still needed two late goals to rescue an unlikely point.
The only other time Aberdeen have opened the scoring in the Clydesdale Bank Premier League this season was against St Johnstone in Perth and that resulted in their only three points of the season.
Brown said: "We have avoided defeat in the last eight matches but we have drawn five of them, which is disappointing.
"It sounds good being eight games unbeaten. But you get six points for winning two games and five points for five draws.
"It`s time to win games, particularly at home. The fans know that. The players know that.
"It won`t be for the want of trying if we don`t because there is a real determination about this group.
"You can see that in the recoveries we have had. I said to them we want to be in the ascendancy and then dig in to retain a lead rather than having to fight back.
"That red army is due a win at home. We have got to get that as early as possible and there is no better way to do it than to beat Hibs and close the gap on them and confirm the first five league games were no fluke."
Wingers Ryan Fraser and Jonny Hayes face late fitness tests ahead of the lunchtime kick-off.
"They have been a major part of the team so it will be disappointing if they don't make it," Brown said.
"But Niall McGinn can play wide. He played the full game in midweek and he needed that because his game depends on being sharp and quick."
Meanwhile, goalkeeper Ben Williams feels he is thriving on the challenge of turning around Hibernian's fortunes.
Hibs will go top of the Clydesdale Bank Premier League - for several hours at least - if they win at Aberdeen following a six-match unbeaten run in the competition.
The new-found resilience is in contrast to two-and-a-half years of struggles at Easter Road which culminated in the 5-1 William Hill Scottish Cup final defeat by rivals Hearts in May.
Williams arrived from Colchester as one of 10 summer signings by manager Pat Fenlon, although captain James McPake and top goalscorer Leigh Griffiths had been on loan last season.
And the 30-year-old believes Fenlon's overhaul is taking shape.
Williams said: "When I came here in the summer the manager explained to me exactly the position the club was in and explained exactly what was needed.
"Although it is still incredibly early days in terms of the season and it`s still a work in progress, it looks like that plan is coming into fruition.
"He has identified the players he wants both in and out of the club. I think he knows what it`s going to take to build a club back to where it belongs."
Striker Leigh Griffiths is set to return after missing the 2-2 draw against Inverness with an ankle injury but resumed full training on Thursday.
Former Carlisle midfielder Tom Taiwo is pushing for involvement in the squad after working on his fitness.
Source: PA
Source: PA