The Toffees have been in excellent form since the Premier League gave them a ten-point deduction for breaching financial rules.
Wins have come against Newcastle and Chelsea in recent weeks, with a trip to north London their latest fixture in a busy schedule.
And fans will be heading back to Merseyside thinking of what could have been as they came ever so close to sealing a draw.
Spurs took the lead after nine minutes as Richarlison, playing against his former club, netted from Brennan Johnson's low cross.
Captain Son Heung-min made it 2-0 soon after to put the hosts in control of the match, but Everton began to fight back.
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The Toffees went into the break the better side, with Spurs lucky to hold onto their two-goal advantage amid a flurry of chances.
Dominic Calvert-Lewin thought he reduced the deficit early in the second-half but his goal was ruled out for a foul from Andre Gomes.
The Portuguese midfielder, who made his first Everton appearance since May 2022, scored with eight minutes remaining on the clock.
Deep into stoppage-time after an onslaught from the Toffees, Arnaut Danjuma came within millimetres of drawing his side level.
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His shot cannoned off the crossbar and onto Spurs goalkeeper Guglielmo Vicario, who probably had little idea of what happened.
Everton therefore came agonisingly close to what would have been a precious point but it wasn't to be.
Spurs were able to hold onto the win to make it three consecutive Premier League victories having previously been winless in five.
Sean Dyche's side remain four points clear of the relegation zone but their win streak in the league has now come to an end.