The Blues were by far the more adventurous side and had several half-chances to score, but it took Jorginho's penalty to separate the teams at the break.
Timo Werner, Mateo Kovacic and Mason Mount all had efforts in the second half to increase the lead, but a combination of last-ditch defending and a lack of accuracy in the finish meant Spurs still had the opportunity to snatch a point late on.
Their best chance fell to Carlos Vinicius, who nodded an effort wide of goal in the closing stages, before Werner almost doubled the Blues' lead in stoppage time.
Here are five things we learned from the game at Tottenham Hotspur Stadium.
Tottenham’s defensive set-up
The first-half showing from Spurs was, quite simply, atrocious. The midfield pivot was sat on top of the centre-backs, offering no outlet when they won back possession and giving Chelsea lots of space to create down the channels.
Spurs' first shot of the game came four minutes in; their next one came just before half-time. After that, there was nothing until the final 10 minutes and a late flurry which yielded two half-decent openings, but absolutely no reward.
In truth, that's what Tottenham deserved. Another big game, at home, against a rival and needing a response and they utterly fell flat in the challenge.
Thomas Tuchel's opening games for Chelsea have been an intriguing mix of players in new roles and slightly altered tactics.
Here, the changes in attack came with Mason Mount operating in a slightly deeper roving central role, neither striker nor a specific No. 10 but a clever and relentless runner bridging the midfield line to the forwards.
Either side of him, Callum Hudson-Odoi was lively early on in the right-sided forward role, Timo Werner looking again marginally improved - though still lacking the instinct of his Bundesliga self - from the left.
Above all else, Spurs had quick combination play, movement off the ball and runners behind the opposition back line; the goals aren't flowing just yet but there's no question they will do soon enough.
Tuchel’s early winners
Who have been the new manager's favourites and big performers, then?
Three games in, Mateo Kovacic has been largely excellent in each fixture. Here he should have scored, or perhaps laid the ball off for an assist, but either way it came at the end of a typically driving, adventurous run whereby he utterly tore apart Spurs' midfield zone by himself.
Elsewhere, it was notable that Marcos Alonso earned another start on the left. He didn't shine here, so maybe another rotation might be expected, but this has to be a big positive for a player who had been marginalised under Frank Lampard.
And the aforementioned Mount showed he has another role he can operate in, creating and working in equal measure, impressing throughout and serving a reminder that those who felt he was only in as a Lampard favourite are drastically wide of the mark.
Champions League chase
Three points here for the Blues moves them into sixth place, two points behind West Ham and four off out-of-form Liverpool.
The champions are the targets to chase down right now - they and Leicester in third - and Tuchel will be optimistic that, with marginal improvements over time and the possibility of a much more clinical edge to come, Chelsea can find the consistency to earn a top-four finish.
They certainly have the forward options, the depth in the squad and the drive from the coach to achieve it - though much could hinge on if Thiago Silva's injury is a bad one.
Three in a row
Liverpool, Brighton and now Chelsea have all beaten Spurs in succession, with the wheels really coming off for Jose Mourinho's side.
They've only scored one goal in that run and hit the target just twice against Chelsea: Son Heung-min with a weak effort from range and sub Erik Lamela curling one late on.
Tottenham now have one win in five, while across the entire season their home form is extremely poor: four wins from 11, eighth in the league by points earned in home matches, as well as the same position in the table overall.
The slump is a painful one and they must pick up quickly to challenge for the silverware they could win elsewhere: West Brom next in the league, then Everton in the FA Cup after that and both the League Cup final and the Europa League resumption to look forward to in the weeks ahead.
It's far from season over just yet, but this run of results must be turned around quickly.
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