The win for Spurs sees them move to within seven points of league leaders Chelsea, and will now be hoping West Ham can secure a result against Antonio Conte's side on Monday night.
When Harry Kane picked up the ball 30 yards out from goal at White Hart Lane and unleashed a shot that whistled past Joel Robles, Mauricio Pochettino's reaction was unremarkable.
Tottenham have now won nine consecutive home Premier League games for the first time while Everton's nine-match unbeaten run in the league came to an end.
Kane took advantage of a catastrophic error from Robles to give his side a two-goal cushion.
At White Hart Lane, Kane, who is now the league's leading goalscorer with 19, had opportunities to complete what would have been his fourth hat-trick in 10 games and was disappointed to miss out.
It would go down as Tottenham's ninth straight Premier League win on their own turf. I think he is doing a good job at Tottenham, but I don't like the questions about how he is doing or what he will do.
Even Everton manager Ronald Koeman couldn't pick between the two in a pre-match press conference, despite the fact Lukaku is his player.
Spurs comes into this game in second in the table, with the chance to close the gap at the top to a single-digit deficit, but they're banged up.
The Argentine coach has turned the North London club's fortunes around since joining from Southampton, with the White Hart Lane side putting in an unlikely title challenge last season.
With Antonio Conte's Chelsea side showing no signs of slipping up, Tottenham, Manchester City, Liverpool, Arsenal and Manchester United appear to be scrapping for second, third and fourth with almost a third of the season remaining.
Harry Kane and Jan Vertonghen are expected to be fit after suffering minor problems against the Potters, while Toby Alderweireld is set to have a late fitness test after he left the field during the game against Stoke with a suspected groin injury.
"And that's all about time and that's what we need to have at Everton". "They try to do high pressing, and we like to".
Whilst Kane may not carry the same class that came with the likes of Klinsmann at Spurs, he makes up for it with his work rate and desire for the team which is just as important as his goals, particularly with the style of football Pochettino likes to play.
Romelu Lukaku may be just 23 years old, but he's already one of the world's best goalscorers.