Twice Spurs led through a pair of fine strikes from Richarlison, who would seemingly have the last laugh against his former club, but twice Sean Dyche's men found the required response, as Jack Harrison got the final touch off a Dominic Calvert-Lewin header before Jarrad Branthwaite's injury-time leveller stole a point for the hosts in dramatic circumstances.
Two players brought on at half time in Spurs' midweek win over Brentford - Pierre-Emile Hojbjerg and Brennan Johnson - were rewarded for their impact with starting roles at Goodison Park, where Richarlison would endeavour to prolong his purple patch against his old club.
Tens of thousands of yellow flyers were held up before kickoff in protest against the Premier League, but Everton fans were soon miffed for on-field reasons instead, as Richarlison took just four minutes to remind the Goodison faithful what they are missing.
Building up with patience down the left-hand side, a well-worked move ended with Destiny Udogie fizzing a low cutback into the feet of Richarlison, who directed an exquisite side-footed volley into the top corner with an air of nonchalance.
The Brazilian unsurprisingly held back his celebrations against his erstwhile employers, who responded well to going behind and began to force a few promising set-piece situations, with a specific tactic in mind.
Dyche's men sought to put pressure on Guglielmo Vicario at every opportunity, and one such instance paid dividends on the half-hour mark, when an inswinging Dwight McNeil corner to the back stick was headed back into the mixer by James Tarkowski, and Calvert-Lewin headed the ball onto Harrison's thigh and in a yard out.
Harrison was backing into Vicario as he flapped at McNeil's delivery, leading to the Italian to remonstrate with referee Michael Oliver - akin to Nathan Ake's winner for Manchester City against Spurs - but the VAR room saw no reason to rule the Toffees' equaliser out.
The febrile Goodison atmosphere had seemingly unnerved the Lilywhites, but just 11 minutes after being pegged back, the visitors were in the ascendancy again, as a cute layoff from Maddison to Richarlison on the edge of the box ended with the South American finding the side of the net with a beautiful curling strike.
Dyche's side - who could count themselves unfortunate to be behind - fashioned one more gilt-edged chance from a corner in added time, but despite being hustled and harried by Harrison again, Vicario brilliantly kept out Ben Godfrey's header with his legs before hooking the ball away while on the ground.
The interval came at an ideal time for Tottenham, who came out for the second period with a bit more bite in the final third, as Maddison and Pedro Porro both stung the palms of Pickford before the hour mark.
Scrappiness was abundant as the game progressed into the final quarter, although Pickford had to be alert to deny Richarlison his hat-trick in the 70th minute after the Brazilian was slipped through by Dejan Kulusevski, and Spurs were doing well to snuff out any potential Everton attacks.
Two Toffees substitutes did combine to carve out an opening in the 88th minute, as Lewis Dobbin's inswinging cross from the left half-space found the run of Chermiti - who may have been in an offside position - but his first-time flick fell straight into the body of Vicario anyway.
As seven minutes of injury time went up on the board, another two replacements were involved in an incident in the Spurs box when Radu Dragusin sent Beto tumbling to the floor, but despite fierce Everton protests, Oliver saw nothing more than a coming together and did not point to the spot.
Dyche's men continued to desperately huff and puff, though, and in the fourth additional minute, their pressure was rewarded, as Cristian Romero glanced a James Garner free kick towards the back post, where Branthwaite arrived untracked to tower above Vicario and head home from close range.
Branthwaite's leveller survived the customary VAR offside check as Everton and Tottenham shared the spoils at Goodison Park for the fifth Premier League game running, allowing Dyche's men to temporarily rise above Luton Town into 17th, while Tottenham stay fourth but are two points behind Arsenal, who have a game in hand.
Tottenham return to their North London base on February 10 for a home date with Brighton & Hove Albion, while Everton are also involved in next Saturday's lunchtime kickoff with a daunting trip to Manchester City.