Only goal difference separates them from 19th-placed Reading and while they remain five points away from safety, Redknapp hopes the conclusion of their three-match losing streak will provide the springboard to climb the table.
"That was our first away win in the league since October 2011. Let's hope we can build on it. There's still a long way to go but that was encouraging," Redknapp said.
"We had a good meeting after the Liverpool match and I convinced the players we can stay up. Everybody else thought I was mad but I do genuinely believe it. We're not doomed, we can turn it around.
"If we keep working hard for the rest of the season we'll win games away and at home. We have to make the most of that. The atmosphere in the changing room afterwards was fantastic, it's the first time I've really experienced that here.
"I said to (assistant coach) Joe Jordan after the game, 'I cant remember having many better games than this one'.