The German side head into the game trailing 3-1 after a first leg defeat in Moscow last week - but Rausch believes the home supporters can play a big part in spurring a spectacular recovery.
Rausch said: "For us, the fans are important and if we score an early goal and wake up the stadium, anything is possible. We need to put everything into the game and we also need a bit of luck."
Big-spending Anzhi came from behind to win in Moscow with goals from Samuel Eto'o, Odil Akhmedov and Mbark Boussoufa cancelling out an early opener from Szabolcs Huszti.
It was Anzhi's first competitive game since mid-December while Hannover have had a busy schedule by contrast, drawing 2-2 at Nurnberg on Sunday in a result that kept them eighth in the Bundesliga table.
Hannover's Mohammed Abdellaoue admitted his side would have to take risks if they are to stand any chance of maintaining their interest in continental competition this season.
The 27-year-old Oslo-born striker said: "We have to be courageous and compete with the conviction that we can do it. Tomorrow is a game of all or nothing, and that is the type of game you live for as a footballer."
The Russian side are without Yuri Zhirkov, who is suspended after picking up his third yellow card in the first leg. Hiroki Sakai and Sebastien Pocognoli are challenging to replace the former Chelsea defender in tomorrow's clash at the AWD-Arena.