Lewis Skelly, 18, finished first-time through the legs of Albania goalkeeper Thomas Strakosha following a sublime pass from Jude Bellingham.
England utterly dominated the ball and went close to a second before the break when Dan Burn, another debutant, headed Declan Rice’s corner off the crossbar.
Kane settled the qualifier with a fine finish after taking down Rice’s hopeful cross, ensuring a smooth evening for new head coach Tuchel.
Here are three England talking points from the game…
Man of the match: Myles Lewis-Skelly
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Lewis-Skelly assured but Burn ragged defensively on debut
If Tuchel’s initial 26-man squad felt flat, his first starting XI still managed to be refreshing, with Burn and Lewis-Skelly – his two wildcard call-ups – both going straight into the side.
At 32, Burn was England’s oldest full debutant since Kevin Davies in 2010, capping a remarkable week for the Newcastle defender, who scored in the Carabao Cup final win over Liverpool here last weekend.
The inclusion of the towering Burn felt in keeping with Tuchel’s desire to build an England side which embodies the best qualities of the Premier League, and the centre-half was predictably dominant in the air at both ends of the pitch.
Towards the end of the first half, he got his head to three corners in a row – the second of which crashed back off the Albania crossbar, leaving Burn so close to back-to-back Wembley goals.
He did, however, also hit his own crossbar in the first half, diverting a cross up and over Jordan Pickford before nervily heading the ball out of the goalkeeper’s hands.
Rollercoaster: Dan Burn had a mixed night
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It was one of several hugely jittery moments for Burn defensively and he was at fault on three separate occasions for half-chances for Albania in the second half, needing Kyle Walker (twice) and Ezri Konsa to bail him out.
Was it nerves, a League Cup hangover or is Burn simply not up to this level (strange as that may seem, given Albania’s quality)?
It is too early for sweeping judgements but, on this showing, you would not want this version of Burn at the heart of England’s defence against a leading international side in the USA, Canada and Mexico next summer.
Lewis-Skelly, by contrast, continued his remarkable breakthrough campaign with an assured display, becoming England’s youngest-ever scorer on debut, at 18 and 176 days – beating a record previously held by Marcus Rashford.
His run to dart behind his full-back for the goal could not have been more contrasting to Kieran Trippier repeatedly cutting inside on his right foot during the European Championship.
Tuchel had admitted to being unsure about calling up the teenager so soon but Lewis-Skelly’s impressive start has boosted his chances of being the long-term answer to England’s problematic left-back spot.
Struggles: Marcus Rashford
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Rashford bright but short of sharpness
You could see why Tuchel immediately restored Rashford to the XI, the on-loan Aston Villa forward lining up on the left of the front three next to Kane and Phil Foden.
Rashford was relentlessly positive, constantly running vertically at his full-back or looking to dart behind the Albanian back four.
He was a threat, and his run and deft pass created a chance for the sublime Bellingham towards the end of the first half.
Rashford, though, still looks short of sharpness and, for all his positivity, he was missing a yard or a touch in the final third.
In time, Rashford could get back to being an important player for England, especially as Kane and Bellingham will always thrive with direct runners, not matter the system, tactics or head coach.
For now, though, it was perhaps premature to throw in a player who has not scored since December 1 ahead of Anthony Gordon and Jarrod Bowen, both of whom were introduced for the final 20 minutes in a double change for Rashford and Foden.
Tuchel may want to keep Rashford “close” but the winger has more to do to prove he has earned a second chance on this scale for England.
70-up: Another England goal for Harry Kane
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New era, same old match-winners
It is too early to say if Tuchel’s plan to transform England into a high-pressing, relentless, Premier League-adjacent international side can work, but there was evidence of the German’s new approach at Wembley – albeit against a limited opposition.
By the interval, the hosts had completed 437 passes – more than in any other first half in any competition since Opta’s records began, underlining Tuchel’s desire to build a progressive, technical team.
There was also evidence of a high press, largely implemented by Rashord, Foden, Bellingham and the impressive Curtis Jones, though Albania’s reluctance to play out from the back meant there were few opportunities for it to take effect.
With the wingers hugging the touchline and Bellingham and Kane staying high, there were also noticeable tweaks from Gareth Southgate’s tenure.
In the end, though, the first game of the new era was settled by moments of brilliance from the same old protagonists: Bellingham, who made the first goal for Lewis-Skelly, and Kane.
That was a reminder that for all Tuchel’s changes to personnel and tweaks to the set-up, getting the best out of England’s two best attackers may well be the key to his hopes of “putting a second star on the shirt” next summer.