Kane came off the substitutes' bench to complete a dramatic late fightback at Villa Park on Sunday by finding the back of the net with a deflected free-kick to ensure Tottenham secured a 2-1 victory.
Tottenham had looked set to slump to a third consecutive Premier League defeat after Andreas Weimann ended Villa's 547-minute goal drought to open the scoring in the first half.
Villa's hopes of ending their five-match losing streak suffered a major blow 25 minutes from time, though, when Christian Benteke was sent off for raising his hand into Ryan Mason's face off the ball in a feisty second half.
The Belgium striker's moment of madness proved to be costly, as Nacer Chadli equalised six minutes from time and Kane rubbed salted into Villa's wounds with a 90th-minute winner.
England Under-21 international Kane now has nine goals in his last 13 games in all competitions, but the in-form striker has not started a Premier League game under Tottenham head coach Pochettino.
Pochettino hinted after the game that Kane may get his chance from the start at home to Stoke City next weekend after his telling impact from the bench.
He told Sky Sports: "Yes, if you score and give the victory it's a perfect situation. We analyse and we select the team.
"It's true that he's getting better since the start of the season and maybe he deserves to play in the next game."
Tottenham had won only one of their last seven top-flight games before their victory at Villa Park and Pochettino stressed that his side are still a work in progress.
"We deserved the victory. The team worked hard and showed their character. In the end, the points are the most important thing," he said.
"No [it was not a relief]. If you have a good result, you are a great manager if you lose you are a bad manager. We have our idea, our philosophy and we need time but it was important to get this result."
