The Rs went into the match on the back of three successive Premier League defeats, while the home side had won their last seven games in all competitions.
Chelsea dominated throughout, but Shaun Wright-Phillips' strike 12 minutes from time secured Redknapp what he believes is one of the greatest results of his managerial career.
After the match, Redknapp told reporters: "I said to Joe Jordan after the game that I can’t remember having many better wins than this one.
“To come here against a Chelsea team who were absolutely flying and after the Liverpool and West Brom defeat, it was a great result for us.
“We changed it up – I stuck Adel up front. He’s never played there before, but he gave us a focal point where we could hold the ball up. It was a good night.
“Liverpool was difficult. The way we set the team up, I felt the players didn’t really understand what we were trying to do. Yesterday we spent a couple of hours with them doing loads of shadow work, so everyone knew exactly where they should be.
“Most importantly, we worked hard. If they all graft, we’ve got a chance.”
Redknapp had hoped to complete his first signing of the transfer window earlier on Wednesday, but the player in question – Joe Cole – now looks set to re-sign for West Ham, much to the disappointment of the Rs boss.
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He added: “I lost a player, Joe, who would have been my first signing, and he probably thought ‘Harry, I love you, but I don’t think you’re going to stay up’, so he’s gone to the Hammers. I thought he’d be good for me, but it’s not easy when you’re stuck down there.
"He’s West Ham, so I understand. West Ham love him – I signed him when he was 11, so he’s gone back home, and I wish him all the success in the world. He’s a great lad. If I’d have been in his position, I’d have found it difficult too.
“I’m not close to getting anybody in at the moment. Joe was the only one I’ve tried to get in for the last two weeks, but that’s about it.”
The former Tottenham boss is optimistic his new side can avoid the drop after picking a first away win in over a year and believes the club’s board are just as hopeful.
He continued: “I had a meeting with them after the Liverpool game, and I convinced them that I think we can stay up. I said that on Sunday and everyone thought I was mad, but I did genuinely believe it.
“It’s the first away win since October 2011, so let’s hope we can build on it. There’s still a long way to go, but it’s encouraging."