Mauricio Pochettino's honeymoon period at the White Hart Lane helm did not last too long, with the pressure ratcheting up thanks in no small part to four defeats in six league matches on home turf.
It was a miserable record which looked set to be extended when Kevin Mirallas put Everton ahead early in Sunday's match, although efforts from Christian Eriksen and Roberto Soldado secured Spurs a much-needed 2-1 win.
That was their third straight win in all competitions, setting up Pochettino's side nicely for Wednesday's trip to in-form rivals Chelsea.
Jose Mourinho's men have been mightily impressive this term, so much so that going through the season unbeaten looks realistic, but Kane believes the suspension of star turn Costa offers a glimmer of light.
"We're full of confidence," the striker said
"Obviously we are coming off three wins in a row now in all competitions, so we'll take that confidence into the game on Wednesday.
"We're looking to get the result
Obviously Chelsea are going to be trying to do the same at home, but they are missing their main man up front
So they have to change a few things, and we're feeling good.
"The Chelsea game is not the be-all or end-all, but it would add to the great momentum we have at the moment if we could beat them.
"That is what we want to do and we will give ourselves the best possible chance."
As well as an upturn in results, Spurs head to Stamford Bridge buoyed by an improved team display.
The Pochettino revolution has yet to fulfil expectations at a club symptomatic with style but on Sunday the team played in the high-pressing, attacking manner he became known for at Southampton.
"We have been working hard, getting our shape together and sliding together, pressing high up the pitch," Kane said.
"I thought we did that well today and obviously it worked well because we got the result in the end.
"We have been working on it recently
We're getting used to it more, getting fitter.
"I thought the lads worked very hard
You saw in the first half we were out of the blocks, trying to get the ball back high up the pitch and that's how we got our second goal."
That winning effort was a particularly important moment for everyone connected with Spurs, given it brought Soldado's 593-minute wait for a goal to an end.
"I am delighted for Roberto to get his goal," Kane said of his team-mate
"He has been a tad unlucky in the recent games, so it means a lot to him to get on the scoresheet.
"Obviously the lads are very happy for him and hopefully he can push on and get a few more."
While Spurs ready themselves for the short trip to west London, Everton will look to get back to winning ways when Hull visit on Wednesday.
The defeat at White Hart Lane ended an eight-match unbeaten streak in all competitions, after which manager Roberto Martinez lamented a lack of fortune.
Sylvain Distin offered no excuses, though, playing down the absence of injured midfielder James McCarthy and the influence of Thursday's Europa League match in Wolfsburg.
"We can't expect to win every game," the Everton defender told the Liverpool Echo
"It's a tough place to come.
"I don't think you can just point your finger at Thursday night - they are tired as well.
"It's easy to read it that way but this is the Premier League
Games are tough.
"We can change this feeling quickly
That's the beauty of the Premier League
We can't dwell on it too much.
"We have to learn from our mistakes and then move on and be ready
There are lots of games coming."
Source : PA
Source: PA