Harry Kane became the 400th player to appear for Spurs when he scored the opening goal in the win over the Toffees.
Kane scored from the penalty spot after being tripped by Jordan Pickford, who had failed to hold on to Matt Doherty's long range effort.
Late in the game, Pierre-Emile Hojbjerg hit a curling strike that took a slight hit off Alex Iwobi but still went in.
The two best chances of the first half went to the visitors, who will be disappointed not to have taken advantage of them.
After racing on to Coady's long ball over the top of the Spurs defence, Gray failed to hit the target and Onana missed the target.
Kane sent a rasping volley straight at Pickford early in the second half but there was nothing the keeper could do about the 29-year-old's spot-kick.
With the victory, the team is level on points with Manchester City and just a point behind north London rivalsArsenal.
Kane has scored in five successive top-flight games for the first time in his career and Spurs have 23 points from 10 league games.
The home side rode their luck in the first half and could have been behind at the break, but they still walked away with a victory.
It wasn't long before Pickford brought down Kane inside the six-yard box with an outstretched arm, giving Spurs a 2-0 lead.
Jimmy Greaves had a Spurs record of 266 goals.
Hojbjerg found the far corner with a shot off Iwobi in the last five minutes.
Richarlison went down clutching his left calf in the second half and was replaced by Yves Bissouma.
The manager spoke of the strength of character of the team before the game.
The visitors were taking no risks in the early stages of the game, with the trio of Iwobi, Onana and Gueye operating deep in front of the back five.
Gray's finish lacked composure, despite the fact that he should have taken the lead after Coady's release.
The same could be said for Onana's wild effort, which came after a lapse in concentration from Hojbjerg.
The second-half was one-way traffic as the Toffees failed to register a shot.
Their four attempts is their lowest total of the season so far.
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