Goals from Jermaine Jenas and Darren Bent were enough to ensure Spurs claimed an impressive triumph over high-flying Villa.
King and fellow centre-back Jonathan Woodgate particularly impressed for the North London club as Villa looked for a way back into the game.
Redknapp was quick to praise 28-year-old King, who suffers with a persistent knee problem that limits his time in training.
Redknapp told Sky Sports: "He is an amazing, amazing footballer. A top, top, top player. Him and Jonathan Woodgate are superb. And I have got Michael Dawson. Three great centre-halves.
Freak"Ledley showed pace. It's amazing. He genuinely doesn't train all week. He came back yesterday for the warm-up and that's it. But he can turn in performances like that. He is an absolute freak."
Of the result, he said: "We are playing well. To come to Villa, which is one of the most difficult places, and win like we did was superb.
"I've been delighted with what we've done since I've been here. I am delighted with the players. Their attitude has been first-class and their work-rate today was great."
Redknapp opted to replace Didier Zokora with Vedran Corluka on 35 minutes after the former had struggled to cope with the quality of Ashley Young.
ZokoraOn the decision, the Spurs manager said: "I played Didier at right-back against (Cristiano) Ronaldo at White Hart Lane and he did fantastic. And against Stewart Downing, and he was fantastic again.
"But today he found it difficult to cope with Young, who is a fantastic player. It was a bit of a problem. He didn't get close enough. And he got booked.
"I made the change and I think Charlie was fantastic. He did superbly - a great job for us."