The London side have lost both of their home games so far, to leaders Monaco and then second-placed Bayer Leverkusen.
The Germans now sit two points above them after winning 1-0 at Wembley on Matchday Four, and Spurs badly need to make up ground this week.
They got a boost in the Premier League at home to local rivals West Ham United on Saturday, turning a 2-1 deficit into an unlikely 3-2 victory when Kane, only recently returned from injury, scored twice in the last few minutes.
"It's a must-win game (in Monaco) and this gives us a big high to go out there and win," Kane told BT Sport after his dramatic double at White Hart Lane.
Spurs manager Mauricio Pochettino added: "The last month has been tough for us and it's fantastic to discover that feeling again for the games ahead.
"The first is a game we must win against Monaco and it's for that reason we need to have the mentality and feeling that we can go to Monaco and win."
Tottenham remain the only unbeaten side in the Premier League, although six draws in their 12 games means they are only fifth in the table, albeit four points behind the leaders.
Monaco are second in Ligue 1, three points off the pace, after a comfortable 3-0 victory at Lorient.
Colombia striker Radamel Falcao continued his fine run with another goal for the principality side and, after hapless spells with Manchester United and Chelsea, would love to remind doubting English fans of his quality.
He scored twice in the last Champions League fixture, an easy 3-0 win against CSKA Moscow, which followed two draws and a 2-1 win in their opening game at Spurs.
Bernardo Silva and Lemar scored in the first half-an-hour against Tottenham while Pochettino's side were still adjusting to Wembley, where they are playing Champions League games as they start construction of a new stadium at White Hart Lane.
The French side now need only a repeat of last season's draw at home to Spurs in the Europa League to qualify for the knockout stage with a game to spare.
(Reporting by Steve Tongue, editing by Pritha Sarkar)
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