A Jermain Defoe penalty and a Gareth Bale goal gave Spurs a 2-1 victory against Chelsea at White Hart Lane just three days after they beaten another of their London rivals Arsenal by the same scoreline at the same venue.
"They were well-deserved wins," Redknapp said.
"We were the better team again, there was no doubt about that. We created all the chances and deserved the points.
"It's a difficult task beating Chelsea, not many teams manage to do that."
The win lifted Spurs into fourth spot in the Premier League table as Manchester City had been beaten 1-0 by Manchester United hours earlier.
"The Man United result went our way tonight but you have got to take advantage of that. We had to make sure we won to get the benefit," the Spurs boss added.
"I still think it's going to be close.
"Villa and Liverpool have it all to do to catch us but certainly Man City have still got a great chance. We have still got to go to City."