Tottenham moved five points clear of fifth-place Chelsea and to within one of Liverpool in third – and still have a game in hand over Jurgen Klopp’s side.
Dele Alli and Kane scored the goals at Wembley as Watford remained six points ahead of the drop zone.
Kane pulled to within four goals of Premier League top scorer Mohamed Salah with his 27th strike of the season.
Tottenham’s form has tailed off in recent weeks and they had gone three games without a win – including the FA Cup defeat to United – before the 2-0 win.
Kane has come in for criticism but he insists he’s in a good place, and he believes Spurs can catch Liverpool – who play Chelsea this weekend after their Champions League semi-final second leg.
The England striker said: “I feel good. I would like to have played better in the last few games – as the whole team would have – but I feel good and I feel sharp.
“Hopefully I can finish strongly like I did last year and go into a big summer. I try to improve every year and last year I got 29 so I’d like to try and beat that first and foremost. We’ll see what happens and in my mind I’m just trying to get to that 30 mark.
“We’ve got a game in hand over Liverpool and if we win that we jump above them as well. It was important just to get the job done tonight and hopefully we can look forward to our final three games now.”
Kane though believes Spurs could have played better at Wembley and thinks they had Hugo Lloris to thank for going in ahead at the break.
He said: “It was good but we could have played better. I thought we could have moved it quicker and we were lucky to be ahead at half-time thanks to Hugo.
“We were a little bit better in the second half but there were still times I felt we could have played it a little bit quicker, especially through the lines.
“We did what we needed to win the game and ease the pressure a bit and we did that. It feels like ages since we last played and our run of form hasn’t been the best.
“When that happens, you want to play straight away and make it right. We’ve had to wait eight days or so [after losing in the FA Cup to Manchester United] and we started a bit slowly but we won the game and we’re happy.”
Mauricio Pochettino was happy to take the result in difficult circumstances and says the performance was secondary on a must-win night.
“I think it was a good night for us,” Pochettino said. “It was important to get the three points as it allows us to be in a good position. It was a must-win game – so important for us. Perhaps we did not play in the way we wanted but got three points.
“During the whole season, 10 months, it is hard to keep playing good football. Watford are a difficult opponent, they played well, created great chances.
“Hugo Lloris was fantastic and showed why he is one of the best in the world. I am happy, three points puts us in a good position.
“The team came back from a difficult loss. They were disappointed after Manchester United. Watford were free to play, no pressure, they are safe, for us it is a massive pressure to take three points.
“Three games ahead, I think we are in a good siutation. To win the games and finish in the top four for the first time in a row would be great for the club.”
Watford boss Javi Gracia admitted he was frustrated with the result following a decent showing.
He said: “When the game finished, you could see we didn’t score and didn’t get points which is frustrating.
“I’m sure we can get more points and more goals in the next game. There were a lot of situations when I arrived but we have tried to improve the position in the Premier League.
“We want to get those three points.”
Former Tottenham midfielder Jermaine Jenas thought Pochettino’s side were tense and lacked the flow they were showing during the early part of the season.
He said: “It was job done, it wasn’t the most vintage performance.
“There was a lot of tension in the stadium that transmitted to the players. There were a few dodgy touches and passing was not on the money.
“They got three points which is the most important thing. They had Chelsea slowly creeping up on them too so they now have an opportunity to start looking upwards rather than behind them.”
