However, Justice Timothy Brewer rejected the case for an interim injunction earlier this year.
The Austrian-headquartered company took the case to the Court of Appeal, which this week overturned Justice Brewer's decision in a majority ruling.
The judges said Drink Red presented Justice Brewer with a "misleading report" from its marketing company.
The report put before the High Court judge was different from earlier versions and statements about how certain style features would be an effective way to "tap into Red Bull's equity" were not included.
The earlier versions of the report - from June 2014 and February 2015 - were discovered by Red Bull after it lost its interim injunction bid.
The Court of Appeal's Justices Christine French and David Collins said the new evidence demonstrates Drink Red's intention to use Red Bull's intellectual property when Drink Red named and marketed its products.
"The original June 2014 report refers repeatedly to Red Bull products, and the subsequent actions of Drink Red demonstrate an intention to erase any evidence of a link between its products and Red Bull's, despite it being clear Drink Red was "piggy backing" on Red Bull's intellectual property," they said.
In my view, there is a serious argument that Drink Red is entitled to take advantage of the popularity of Red Bull and vodka with a rival RTD using the name RED, with "R" reversed.
The judges were convinced Justice Brewer would have granted the interim injunction had he been aware of this evidence.
They granted Red Bull's appeal and restrained Drink Red from selling or advertising its product under the brand "ЯED" or any other trade marks similar to Red Bull's.
Justice John Fogarty, one of the judge's hearing the appeal, disagreed with his colleagues.
"Vodka Red Bull (or "Red Bull and Vodka") is a popular drink for young people at bars. But you cannot buy ready-mixed Red Bull and vodka in ready-to drink (RTD) form. This is a gap in the market that the new entrant respondent sought to exploit. In my view, there is a serious argument that Drink Red is entitled to take advantage of the popularity of Red Bull and vodka with a rival RTD using the name RED, with "R" reversed," he said.