Shaun Wright-Phillips came off of the bench to net the only goal of the game against his former club.
The three points move the Super Hoops level with Reading, and to within five points of safety.
Redknapp was happy with his team after the game, saluting their attitude on the pitch:
“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.
“I’m just really pleased with out 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.”
Adel Taarabt was deployed in a central forward role for the second-half, a move which Redknapp was delighted with:
“I pulled him over yesterday and told him I’d play him up front,
“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.”