Shaun Wright-Phillips came off the bench to score the winner with 12 minutes remaining to secure their first league away win for 14 months and their first triumph at Stamford Bridge since 1983.
The three points also got them level on points with Reading at the foot of the Premier League and five points from safety to give them a huge boost in the fight for survival.
"They worked their socks off tonight and you get your reward if you work like that - and that's what we did," Redknapp told Sky Sports.
"It was a fantastic performance. We restricted Chelsea to very few chances and we deserved it.
"We had good opportunities as well and if the final pass had been better.....we hit some final sloppy passes but then we got that fine goal."
QPR suffered a setback when Junior Hoilett limped off early on, setting up the introduction of Wright-Phillips, but they also benefited from playing Adel Taarabt as a lone striker.
"I pulled him over yesterday and told him I'd play him up front," Redknapp added. "I told him to hold the ball up and wait for us to join him.
"We worked on it for a couple of hours in training. It was a gamble really but the shape was good. I'm not even sure if he's played up front before."
The three points were all the more pleasing for the manager, coming four days after the 3-0 home defeat by Liverpool.
"We had a good meeting after that match and I convinced the players we can stay up," Redknapp said.
"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.
"The atmosphere in the changing room afterwards was fantastic, it's the first time I've really experienced that here."
And with Redknapp's next league match against his former club Tottenham on 14 January, he said: "I'm just really pleased with our first away win for over a year.
"They've set the standard tonight and if we're going to get out of this mess then they have to work as hard as that - not just once but every week."