Newcastle secured a vital point in their quest to avoid relegation as Tottenham saw a chance to climb into the top four go begging.
Both centre forwards on display came close to breaking the deadlock in the early stages.
Kane saw a fizzing near post strike parried wide by Martin Dubravka, while Dwight Gayle forced a spectacular double stop from Hugo Lloris.
Japhet Tanganga and Davinson Sanchez both saw poor clearances blocked before Sean Longstaff rolled a delightful pass to Joelinton.
The Brazilian has been shy in front of goal all season but made no mistake here, slotting past Lloris to make it 1-0.
The lead lasted barely a minute when Spurs hitman Harry Kane was in the right place at the right time to punish slack defending.
Giovani Lo Celso’s through ball was cleared by Emil Krafth straight at the feet of Kane. The ricochet left Dubravka in no man’s land to allow Kane the simple task of tapping home from a yard.
The turnaround was completed in the 34th minute when the deadly Kane bagged his second.
A lovely reverse pass from Tanguy Ndombele set Kane free before the England captain fired hard and low into the bottom corner.
Newcastle's lead didn't last long! 😳
Terrific turnaround from Tottenham, and Harry Kane is at the double! 🔥
Emphatic finish from Spurs' main man…
— Sky Sports Premier League (@SkySportsPL) April 4, 2021
Miguel Almiron menaced the Tottenham backline straight after the interval, though the impressive Lloris was again on hand to keep the Magpies attackers at bay.
The visitors were seemingly content to soak up pressure and hit Newcastle on the break. Entering the final half hour, the contest was finely balanced.
Newcastle were dominating the shots statistic, at one point outnumbering their fancied opponents 15 to four.
The better chances were falling for Spurs, however, with Tanganga coming close to putting the game beyond reach.
Dubravka’s punch from a corner went more up than out. Tanganga steamed in to head towards goal, but with the goalkeeper beaten, Almiron stood firm to head off the line.
Newcastle finally crafted the opportunity they sought, but Joelinton couldn’t match Kane’s tally when side-footing agonisingly wide from eight yards out.
Actually think this has been one of Joelinton's best games for #nufc – not saying much admittedly – but what an opportunity.
Can't say #nufc haven't had the chances to be at least level if not in front today.
This is where Wilson is so sorely missed. So clinical in comparison
— Ciaran Kelly (@CiaranKelly__) April 4, 2021
Kane came within the width of the post of bagging a hattrick from a fast-break, with that miss would proving costly seconds later when Joe Willock levelled the scores.
Resolute defending denied Almiron from close range, but the ball fell to the on-loan midfielder who fired in off the crossbar to make it 2-2.
Both sides sought a winner but were made to settle for a point apiece in a thoroughly entertaining contest at St. James’ Park.