Spurs struggled on a bumpy pitch, where professional rugby games are also hosted, and the home side took full advantage, taking the lead through Padraig Amond in the 38th minute.
But eight minutes from time, in-form England striker Kane equalised when, after Spurs had won a corner, he tapped in from close range following an excellent flick-on from South Korean Son Heung-Min.
The France worldwide has been the subject of plenty of criticism from Spurs fans on social media and he was unable to change the opinions of many during their match in Wales.
The first chance of the historic encounter came around in only the 4th minute of time.
Joss Labadie did well on the right flank and squeezed a low delivery into the penalty area which fell to the unmarked Frank Nouble, but the former West Ham forward inexplicably fired over from 12 yards. "But they are a quality side and in the second half we couldn't really get at them".
Tottenham manager Mauricio Pochettino kept some first-team players in reserve - among them Dele Alli and Son - but the presence of Kane, Eric Dier and Jan Vertonghen showed this was a game Spurs were taking seriously.
LIVE cricket score and updates, Australia vs England, 4th ODI at Adelaide
The final match in the series takes place tomorrow, the first sporting event at a new 60,000-seater stadium in Perth. Hazlewood and Cummins's opening spell reduced England to 8 for 5 in the seventh over.
Nottingham Forest's FA Cup run ended just one round after they knocked out holders Arsenal courtesy of a 2-1 defeat by Championship rivals Hull.
"I hear in five years here that the FA Cup is magic".
Although it eventually led to correct decisions being made, the time it took, with nearly four minutes elapsing between Mohamed Salah being fouled and Craig Pawson awarding a penalty which Roberto Firmino missed, left supporters and players on all sides angry and frustrated.
- Robbie Willmott has assisted seven goals for Newport in all competitions this season, more than any other Exiles player.
Mike Flynn: "I'm absolutely gutted for them because they scored so late". But it's about in the next few days to see if we have some possibilities with some players.
Spurs showed precious little evidence of occupying a division three rungs higher in the English football pyramid, particularly in the first period when Newport started with great intent and looked far more threatening. "We will see what happens in the last few days". "I hope we have learned today that we have to fight to win things".