Michael Keane's late screamer from distance helped Everton claim a point against Tottenham on Monday night as Abdoulaye Doucoure and Lucas Moura were sent off in a frantic Premier League clash.
The Toffees spurned good chances through Doucoure and Idrissa Gueye before the former was sent off for shoving his hand into Kane's face.
The England captain, who had a shot cleared off the line and a header skim wide in the first half, netted his 22nd league goal of the season from the penalty spot after Keane brought down Cristian Romero.
However, Spurs couldn't extend their advantage and were left in the lurch when substitute Lucas Moura cracked Keane's ankle to be dismissed himself. Keane dusted himself off and scored a belter - his first league goal of the season - to earn Everton a vital point in the 90th minute in their fight against relegation.
The hosts came quickly out of the traps against their sluggish visitors as they made space on the left before Demarai Gray curled just wide of the far corner.
Spurs' first attacking foray saw right wing back Pedro Porro creep behind Everton's backline but the Spaniard's fired ball across goal was batted away by Jordan Pickford. Tottenham robbed the ball in midfield soon after and a chance generously fell to Kane, who saw his goal-bound shot blocked by Michael Keane.
Kane got another sight of goal as Spurs switched play quickly to Ivan Perisic. The Croatian's cross found the striker but his header drifted wide of the far post.
Everton put together spells of pressure punctuated by the furious groans that have become familiar at Goodison Park whenever their forward ventures lacked ambition or polish, with the game motoring at an enjoyable pace midway through the first half.
Murmurs of discontent rattled around the ground again when Doucoure got too much on a header when unopposed. That was arguably the half's best chance, but no shots on target were managed during the first 45 minutes.
Eric Dier was caught unaware on the edge of his box a minute after the restart, but Gueye couldn't add the composed finish his high pressing deserved.
The game took a large swing towards Tottenham's favour when a scuffle next to the dugouts ended with Doucoure pushing his hand into Kane's face, leaving Everton a player down and Dyche with a number of choice words for the fourth official.
From that point onwards, the game's pattern was set; Everton sat deep looking to keep Spurs out while the visitors hammered on the door.
The Toffees couldn't hold out for too long, however. Romero nipped the ball away from Keane, whose tired challenge brought the Argentine defender down. Kane made no mistake against England teammate Pickford, drilling into the bottom corner as the goalkeeper dived in the opposite direction.
That goal did spark a revival from Everton. Gueye forced Hugo Lloris to tip a long shot over the top before the Frenchman got down to hold Keane's header.
Everton heaved a load of pressure onto the Spurs backline before being gifted a route back into the game late on. Substitute Lucas was late into a challenge and snapped Keane's ankle, swiftly being given his marching orders just six minutes after his introduction.
With almost the next move of the game, the hosts snatched their point. The ball fell to Keane and the centre back leathered his effort past Lloris in true Vincent Kompany style, seeing his shot whizz into the far corner to send Goodison into raptures.
The result moves Everton up to 15th though still just a point above the relegation zone, while Spurs go into fourth having played too games more than both Newcastle and Manchester United, who sit directly above and below them in third and fifth respectively.
Everton player ratings (4-5-1)
GK: Jordan Pickford - 6/10 - Wasn't peppered with shots at goal but couldn't read Kane from the spot.
RB: Seamus Coleman - 6/10 - Strong and bullish in defence but unsurprisingly brought off when Everton needed a goal.
CB: Michael Keane - 7/10 - Vital clearance early on stopped Kane putting Spurs ahead. Bit of a lazy leg handed Spurs a penalty but he made amends with a wonderful strike from distance to equalise.
CB: James Tarkowski - 7/10 - Was a constant threat from set pieces, winning a lot of headers.
LB: Ben Godfrey - 7/10 - Another strong presence out wide that stopped Spurs finding too much fluidity. Got the assist for Keane's strike.
RM: Alex Iwobi - 6/10 - Drifted into space and found some encouraging positions but the lack of end product was again an issue.
CM: Abdoulaye Doucoure - 4/10 - Spurned a great opening when heading over. Got baited in by Kane and retaliated to leave his side a player down.
CM: Idrissa Gueye - 6/10 - Won the ball off Dier but couldn't keep his cool to finish.
CM: Amadou Onana - 6/10 - Helped put Spurs under the cosh with some decent pressing.
LM: Dwight McNeil - 6/10 - Set-piece delivery might have hurt Spurs a lot more on another day.
ST: Demarai Gray - 6/10 - Better when Everton kept the ball on the deck and struggled to hold it up when they hoofed it long.
Substitutes
Vitalii Mykolenko (77' for Coleman) - 6/10
Ellis Simms (77' for Coleman) - 6/10
Tom Davies (84' for Gueye) - N/A
James Garner (84' for Onana) - N/A
Manager
Sean Dyche - 6/10 - Everton couldn't take control of a frantic encounter. However, Dyche kept his cool and made decent tweaks before Keane bailed him out with a wonderstrike.
Tottenham player ratings (3-4-3)
GK: Hugo Lloris - 7/10 - A little sketchy at the start of his return from injury but commanded his box much more confidently as the game wore on.
CB: Cristian Romero - 7/10 - Didn't have a physical battle to engage with among Everton's forwards.
CB: Eric Dier - 5/10 - A few calamitous moments, including gifting Gueye an excellent chance.
CB: Clement Lenglet - 6/10 - Not physical enough at times but didn't always need to be.
RWB: Pedro Porro - 6/10 - Looked a threat out wide and when arriving into the box.
CM: Oliver Skipp - 6/10 - A little wasteful in possession. Turned well in tight spaces.
CM: Pierre-Emile Hojbjerg - 6/10 - Did well to read a few Everton attacks and make important interceptions. Not inventive enough in possession.
LWB: Ivan Perisic - 6/10 - Set up Kane with a good cross but end product was often lacking.
RF: Dejan Kulusevski - 6/10 - Flittered around on the periphery of the game and constantly looked to dribble forward, sometimes to his detriment.
ST: Harry Kane - 7/10 - Unlucky not to give Spurs the lead and then headed a good chance wide. Kept his cool from the spot to hand the visitors the points.
LF: Son Heung-min - 5/10 - Tried to make himself available but touch was off and never looked like scoring.
Substitutes
Davinson Sanchez (77' for Lenglet) - N/A
Lucas Moura (82' for Son) - N/A - Subbed on, horrific challenge on Keane, sent off. Why doesn't he play more, eh?
Manager
Cristian Stellini - 4/10 - Spurs needed to seize the moment with a player's advantage but instead lost their heads as Lucas evened the playing field. Not a great look for Stellini.
