Luck is on his side too, with his first goal from Son Heung-min's delivery soon after halftime that put Spurs 2-0 ahead looking fractionally offside.
Kane grabbed Spurs' second goal just after the break as he latched on to Heung-min Son's cross, finishing from close range.
Fifth-place Spurs moved level on points with Liverpool, whose game in hand is against Manchester City at Anfield.
To hit 20 goals at this stage of the season in the premiership is incredible @HKane running out of words a complete goal machine.
Eriksen played the killer a pass, an absolutely brilliant ball out wide to Serge Aurier and he took one touch before delivered what appeared to be a shot.
It was not necessarily an fantastic performance from Kane, but to grab two goals despite not performing at his best shows just how clinical and important the Spurs talisman is.
Jimmy Greaves is Tottenham's record goalscorer in all competitions with 266 and Pochettino is pleased Kane has a long way to go before he breaks it. In doing so, Son joined Jermain Defoe as the only Tottenham player to score a goal in five consecutive home matches.
It is easy to expect more goals from Kane today at odds of 2-1 to be the first scorer.
On the day it was revealed Kevin Keegan had returned as manager, Emre was brought back into the team for the cup replay against Stoke and with Newcastle one goal up, managed to get himself sent off after 29 minutes.
Kane then forced Jordan Pickford into a strong save down to his left at the end of a quick Tottenham counter, and the hosts' strong response to the scare Rooney provided was quickly rewarded.
"The disappointing thing for us is, what would the game have finished like had we scored the first goal when Wayne's got disallowed?" I think he's happy there.
Kane - from an unorthodox, somewhat fortuitous finish, added his second, this time from a perfectly whipped in Eric Dier cross.
"I thought he was good and he's experienced a hard game, and there won't be many more hard ones to play away from home than against Tottenham" Allardyce said.