Tottenham boss Redknapp hails exciting past week for club
The results also mean Spurs are back in the Champions League places, with their victory over Arsenal in midweek backed up with goals from Jermain Defoe and Gareth Bale, while Chelsea had John Terry dismissed before pulling one back through Frank Lampard.
"They were well-deserved wins," he said.
"We were the better team again, there was no doubt about that. We created all the chances and deserved the points.
"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.
"It's a difficult task beating Chelsea, not many teams manage to do that."
Redknapp feels the race for fourth will go to the wire.
He 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."