Another sublime performance saw Spurs make club history on Saturday night, marking a 12th straight with at home for the first time, while they have also recorded seven consecutive Premier League victories for the first time in 50 years.
Mousa Dembele opened the scoring with a close-range strike in the 16th minute and Son Heung- Min's cool finish doubled Tottenham's lead three minutes later.
It was nearly the ideal game for Spurs as it witnessed, four goals, a clean sheet, no injuries and even the heartwarming sight of substitute Vincent Janssen scoring his first ever Premier League goal from open play.
Tottenham boss Mauricio Pochettino admits Chelsea are still favourites for the Premier League title despite the "pressure" being on them to win against Manchester United.
Spurs have not lost a game at home in the league and their recent win puts them within four points of Chelsea.
The icing on the cake came from substitute Vincent Janssen, making it four with nearly the last kick of the game from close range.
Redknapp admitted that while Spurs are firing on all cylinders right now, they will need a dramatic slip up from Chelsea to get their hands on the Premier League title.
Manchester City moved above Liverpool into third after they registered an impressive 3-0 win away at Southampton, with captain Vincent Kompany on the scoresheet.
The Italian said: "I think that the impact was very tough today, but when you play at Old Trafford it is normal to have this type of impact against a really strong team as United". Of course it's a different competition so it's hard to say, but it's a big game for us, a big game for the club, a massive semifinal and you never know.
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But Pochettino insists his side wasted too much energy focusing on their rivals and now feels Tottenham are more equipped to ensure the title chase continues until the last game of the season.
Kane had scored five goals in his previous three appearances against Eddie Howe's side and there was an inevitability when he made it 3-0 on 48 minutes.
Victories for Swansea and Hull on Saturday would draw them further into the relegation battle with six games left to play.
"It's good to be consistent as a striker", Kane told BT Sport.
"It could be a big thing psychologically", Kane said.
"It's all done now and we got the three points which is important for us and now we see what happens tomorrow", the Argentine added.
Pochettino believes that has helped and he also flagged up former Leicester manager Claudio Ranieri's recent comment that the whole world had been rooting for the Foxes last season.
"3-0, 4-0, it's important to keep possession, to score goals and that is the mentality we are building".
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