Scotland face New Zealand in Sunday's EMC Test at Murrayfield.
The odds are stacked against a Scotland side which claimed victories in Australia, Fiji and Samoa in June at the end of a torrid season which featured a group-stage exit from the Rugby World Cup and a RBS 6 Nations whitewash.
The All Blacks' most recent loss came in August 2011 against Australia in their final match before the home World Cup which they won, while they have not been beaten on an end of year northern hemisphere tour since 2002.
The tourists are also seeking to erase the memory of their last Test, the 18-18 draw with Australia on October 20 when they missed out on a record-equalling 17th successive win and failed to score a try for the first time in 105 fixtures, since August 2004.
Despite New Zealand having a point to prove, Brown believes in his team as he prepares to lead Scotland out for the first time in his 50th international.
The 30-year-old Saracens number eight told Press Association Sport: "It's a one-off game. We know it's going to be incredibly hard, but it's 15 on 15. We just need to go out there and perform as best as we can and make Scotland proud.
"We've worked very hard. I placed a real emphasis on guys all knowing their roles and knowing exactly what's expected of them in each aspect of the game.
"I feel confident that all our guys have done that. It's now just a case of going out there, doing that and working incredibly hard.
"For us one of the main things is to put them under pressure and to not give them anything easy.
"In the past in the first half we've probably gifted them a few scores.
"It's about going out there, working hard and making them really have to fight for anything that they get."
Scotland have rarely run New Zealand close, drawing twice in 28 Tests.
Since Brown's international debut, Scotland have met four times - the same back-row playing in three of the fixtures - and Scotland have scored 19 points in total, to their opponents' 160.
The All Blacks won the most recent fixture 49-3 at Murrayfield two years ago.
Brown is an indomitable spirit, a tireless member of Scotland's pack, and is certain to lead by example from the front.
New Zealand expect stereotypical Scottish traits like never giving up, but suggested they had not checked the Scotland team 48 hours before kick-off.
"They're the world champions and they've decided to focus on themselves," Brown said.
"That's entirely up to them. They've got the results to back it up.
"It's just up to us now to us now to make sure that we put them under pressure.
"We know what we've got to do. We've got a plan of how we want to start the match. It's now just a case of going out there and implementing it."
New Zealand named their team today.
Brown added: "It's very strong as we always knew it would be. Whatever side they put out will be very, very tough.
"They are fortunate that in their country they have probably got 50 or 60 international-quality players, so any team they ever put out will be very strong, but we're looking forward to it."
Brown has an intimate knowledge of New Zealand rugby after being invited to Christchurch while former All Black captain Todd Blackadder was coaching in Scotland.
He spent two months there during the university summer break as he studied Applied Sports Science at Edinburgh, a course which cyclist Sir Chris Hoy also studied.
Brown added: "I went over there in 2002. We went over and played for a team that was coached by his uncle and I actually stayed with his mum as well.
"It was a really interesting two months and an experience I really enjoyed.
"It was a huge honour. I was living in his home town and just to see the huge respect with which he was held was incredible."
Brown did not forget the experience and, nine years later, took time out from Scotland's World Cup campaign to surprise Blackadder's mother and present her with flowers.
He is hoping for another memorable experience on Sunday.
"It's a big day, but it's not something I'm focusing on," he added.
"I think it's the sort of thing I'll look back on when I'm old and fat and I'll hopefully have very fond memories of."
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