Following frustrating draws against Partizan and Besiktas, Erik Lamela grabbed a brace, including a stunning rabona effort, while Kane hit a hat-trick for 10-man Spurs - who had Hugo Lloris dismissed late on.
Kane was required to replace the Frenchman in goal and, while he fumbled in a free-kick to make it 5-1, the goal failed to diminish from a positive evening as Mauricio Pochettino's men moved level top in Group C with Besiktas, who hammered Partizan 4-0 in Belgrade.
Sparta Prague saw off Slovan Bratislava 3-0 in a Group I fixture that saw disruptions due to crowd trouble in the first meeting between the sides since the break-up of Czechoslovakia in 1993.
The game was suspended after 42 minutes when fans clashed but resumed shortly after - second-half goals from David Lafata, Tiemoko Konate and Ladislav Krejci ensuring Sparta's victory.
Elsewhere in Group I, Young Boys ended Napoli's winning start to the competition with a 2-0 success, while Juan Manuel Vargas maintained Fiorentina's winning start against PAOK in Group K as Guingamp and Dinamo Minsk drew 0-0.
Standard Liege and Lille were held to stalemates at home against Sevilla and Everton respectively, with Feyenoord unable to take advantage of the Spaniards' dropped points in Group G.
The Eredivisie side fell to a 3-1 defeat against Rijeka, while Wolfsburg now sit a point behind Everton in Group H after hammering Krasnodar 4-2 - Kevin De Bruyne scoring twice in Russia.
Trabzonspor bolstered their qualification hopes with a Group L win against Lokeren and AaB replaced Dynamo Kiev at the top of Group J courtesy of a 3-0 victory over the Ukrainians in Aalborg. Steaua Bucharest also sit on six points after beating Rio Ave 2-1
Qarabag beat Dnipro 1-0 to cut the gap to Group F leaders Inter, who drew 0-0 with Saint-Etienne, while Torino are the new Group B leaders after edging HJK 2-0 with Club Brugge only able to draw with Copenhagen.
There were goals galore in Group A as Villarreal hammered Zurich 4-1 and Ibrahima Traore scored his first goals for Borussia Monchengladbach - his brace helping the Bundesliga side to a 5-0 win against Apollon.
Celtic and Red Bull Salzburg pulled further away at the top of Group D with wins over Astra and Dinamo Zagreb - Alan scoring a hat-trick for the Austrian side - while Dinamo Moscow edged closer to progression from Group E by seeing off Estoril 2-1.
Yohan Tavares' goal for the Portuguese side proved a consolation with 10-man PSV held to a 1-1 draw at home by Panathanaikos.