Virat Kohli's side have not lost a home series since late 2012 but have struggled outside the sub-continent, beaten 2-1 in South Africa and 4-1 in England this year alone.
The four-test series in Australia will be the last chance in 2018 for India to match their formidable home form with success abroad and show why they are the world's top-ranked side in the longest format of the game.
The touring side have already taken a firm step towards what would be their first series triumph in Australia by winning the opening test in Adelaide by 31 runs.
"India are already the number one side in the world and the one thing that they still have to prove to everybody is that they can win away from home," Butcher, 46, told Reuters in an interview.
"They had a chance to do it in South Africa, couldn't manage it. The scoreline in England perhaps was a little bit flattering to England but still they lost 4-1.
"They still have to get that monkey off their back of not being able to win away from home, outside of the subcontinent. This would be absolutely huge and they will be undisputedly the best side in the world if they do it."
Winning a test series in Australia is still among the toughest tasks in cricket and India have returned empty-handed from their previous 11 attempts over the last 70 years, winning just five out of 44 tests Down Under.
They will, however, fancy their chances of breaking the duck against an Australian team yet to recover from a ball-tampering scandal that led to bans for former captain Steve Smith, opener David Warner and batsman Cameron Bancroft.
Butcher, who is a panellist for broadcaster Sony Pictures Networks, thinks there is no doubt of the impact that loss has had on Australia's batting.
BATTING STRUGGLES
"They got four very, very good bowlers in their side. It's a fabulous bowling attack but at the moment they are struggling with batting," Butcher said.
"You put in Steve Smith and David Warner in that team and they are a bloody good side again.
"But certainly this team at the moment isn't a patch on the teams I have played against in the 90s and the early 2000s. That's the way it is sometimes.
"You take Kohli and Pujara out of the Indian side, they are not going to find things quite so easy."
The second test begins on Friday at the new Perth Stadium, which has a drop-in pitch and succeeded the WACA as the city's premier venue for internationals.
Butcher, who was twice a losing Ashes tourist during his 71-test career, said the toss would be crucial with the Perth Stadium head groundsman Brett Sipthorpe keen to produce a fast, bouncy wicket.
"It's not going to be a cakewalk. India might win the series but it's not going to be easy," Butcher added.
"The toss on Friday is going to be hugely important. On this pitch they have never played a test match before.
"I have seen in the one-day internationals there's lot of pace and lot of bounce.
"Both quick bowling attacks will enjoy bowling on it. One thing is for sure, it's going to be a fabulous series.
"India are a very, very good side. They do, indeed, stand their best chance of winning in Australia ever.
"But there will be a backlash in Perth and if the pitch turns up to be a fruity one, whoever scores the most runs in the first innings will probably win the game again."
(Reporting by Sudipto Ganguly; editing by Nick Mulvenney)
