The dreary grey skies across Merseyside perfectly typified the mood among both clubs, with the Toffees sitting 16th and Spurs occupying 15th heading into this clash.
The hosts had won only one of their last 12 league games, while Ange Postecoglou’s side had suffered seven defeats in their previous 11.
David Moyes’ side began the game brighter and took a deserved lead when Idrissa Gueye threaded the ball through to Dominic Calvert-Lewin, who bamboozled the Tottenham defence with his close control before clinically firing past Antonín Kinský.
It was the 27-year-old’s first PL goal in 17 appearances and ended Everton’s sobering run of three league games without a goal.
There was an encouraging response from Spurs, who should have restored parity when Son Heung-min fired straight at Jordan Pickford after being picked out by Dejan Kulusevski in the box.
Spurs were looking porous at the back and had their blushes spared when Kinský tipped Gueye's shot onto the post.
But the Toffees soon doubled their lead courtesy of another superb finish – this time from Iliman Ndiaye.
The Senegal international rifled a ferocious finish into the roof of the net after shrugging off Radu Drăgușin’s challenge, before Archie Gray turned the ball into his own net from James Tarkowski’s headed cut-back in first-half stoppage time.
This was very much uncharted territory for the hosts, who hadn’t held a lead of three goals at HT in a PL home game since a 6-3 win over Bournemouth in February 2017.
In truth, the Toffees may have fancied their chances of scoring six here, judging by the calamitous nature of Tottenham’s defending.
After the restart, Vitaliy Mykolenko blazed his attempt over the bar after being teed up by Ndiaye, shortly before Calvert-Lewin turned and shot wide from Jesper Lindstrøm’s cross.
There was to be no further punishment for Postecoglou’s men, who did manage to net a fine consolation goal through Kulusevski’s sublime lofted finish before Richarlison made it a nervy end to the match when he slid home Mikey Moore’s excellent delivery.
Nonetheless, this was ultimately a chastening afternoon for the North Londoners after succumbing to their 12th league defeat of the season.
Meanwhile, this result for Everton moves the Merseysiders four points clear of the bottom three and gives them some much-needed breathing space in the battle to preserve their top-flight status.