The striker pounced from close range to provide the finishing touch as Heung-Min Son flicked on Christian Eriksen’s corner in the 78th minute.
It was no less than we deserved after dominating possession - with 65 per cent in total - and chalking up 24 efforts at goal, but the Azerbaijani champions showed just why they’d only conceded one goal in five European matches ahead of this fixture.
Dele Alli struck the post and Qarabag goalkeeper Ibrahim Sehic tipped Son’s shot onto the crossbar before Kane finally made the telling breakthrough.
Mauricio Pochettino fielded a strong side with three changes from the win over West Ham on Sunday. Ryan Mason returned in place of Mousa Dembele in midfield, while the full-backs were swapped with Ben Davies and Kieran Trippier coming in for Danny Rose and Kyle Walker respectively.
It was a crisp night as the teams were greeted by thousands of flags in the stadium while credit must go to our supporters who made the long journey east and did their best to make themselves heard over the vociferous home support.
Mason tested the gloves Sehic early on as we enjoyed the better of the early possession. The midfielder had obviously packed his shooting boots as he blazed over with another effort from distance with 10 minutes gone.
The best chance of the opening exchanges came five minutes later when Dele Alli almost rounded off a fine move but shot wide after good work from Trippier.
In the return fixture, it had been Qarabag who started the livelier yet they were subdued early on at the Tofig Bahramov Stadium with Hugo Lloris left as a spectator for long spells. The home side were happy to get men behind the ball and invite pressure by staying compact and organised.
It was not until the 28th minute that Lloris was called into action with a straightforward low stop to deny Afran Ismayilov.
We were completely dominant in terms of possession but were finding it hard to unlock the Qarabag back four. Alli came close with a header from a corner as the half ticked towards a conclusion with the scores still level.
We did have a late scare when the home side broke away after clearing one of our corners but Dani Quintana made a mess of the opening by scuffing a shot that Lloris palmed away.
It would remain goalless, though, as both sides made their way down the tunnel for the interval.
The second half began in much the same manner as the first as we saw plenty of the ball but few openings. The feisty Richard Almeida dragged a shot wide from distance for the home side, as did Eriksen for us as we continued to knock on the door.
Kane was clever with his movement but was forced to play in tight spaces as he was surrounded by black shirts in and around the Qarabag box. The England striker did well just after the hour mark to pick the pocket of Almeida and feed Alli but the midfielder’s shot was comfortably gathered by the goalkeeper.
A minute later Kane rifled a shot into the side-netting as he looked intent on breaking the deadlock.
We were getting ever-closer as Son rattled the bar from the edge of the box shortly afterwards via a deflection as we set up camp in the Qarabag half.
Eric Dier was next to take aim with Sehic scrambling his long range effort behind before Kane saw another shot deflected away as we forced a long series of corners.
The home side refused to roll over, though, as Quintana brought the best out of Lloris with a sharp breakaway.
The one-way traffic continued, however, as Alli was next to rattle the woodwork with a cushioned volley after a great ball in from Toby Alderweireld before Kane was denied by a stunning save from Sehic.
Finally the deadlock was broken in the 78th minute - and it was Kane who hit the target. Son flicked on an Eriksen corner, allowing the England international striker to nod in from close range.
That really knocked the stuffing out of the home side and the only efforts of note in the final 10 minutes came from Eriksen - one left-foot shot that zipped just over and a free-kick that sailed into the wall.
The final whistle saw us march on into the round of 32, having assured ourselves of a place in Group J's top two positions.
Qarabag (4-2-1-3): Sehic, Medvedev, Huseynov, Sandygov, Agoli (Armenteros 55); Garayev, Almeida; Quintana; Taghiyev (Chumbinho 65), Poepon, Ismayilov (Mammadov 80). Substitutes (not used): Veliyev, Michel, Gurbanov, Yunuszada.
Spurs (4-2-3-1): Lloris (c), Trippier, Alderweireld, Vertonghen, Davies; Dier, Mason (Carroll 72), Alli, Eriksen (Onomah 90+1), Son (Clinton 80); Kane. Substitutes (not used): Vorm, Wimmer, Townsend, Winks.
Goals: Spurs – Kane 78.
Yellow cards: Qarabag – Almeida 44, Garayev 88.
Referee: Tasos Sidiropoulos (GRE).