Jose Mourinho made a winning return to management as Tottenham withstood a West Ham fightback to win 3-2 at the London Stadium.
Spurs had not won an away Premier League game since January 20 at Fulham, but first-half goals from Heung-Min Son (36) and Lucas Moura (43) put them in a commanding position.
- Jose Mourinho analyses first Spurs win - Full transcript
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Harry Kane extended Tottenham's lead with a trademark header four minutes after the restart to move above Martin Chivers in third place on the list of the club's all-time scorers on 175 goals.
West Ham reduced the deficit through substitute Michail Antonio (73) and Angelo Ogbonna headed in a late second (90+6), but Spurs held on to temporarily move up to sixth place before ending the day in ninth.
The pressure increases on Hammers manager Manuel Pellegrini, whose side have taken just two points from their last 21 available, and sit 16th.
West Ham: Roberto (4), Cresswell (5), Fredericks (5), Diop (5), Ogbonna (5), Rice (6), Noble (5), Snodgrass (6), Yarmolenko (4), Anderson (3), Haller (5).
Subs: Sanchez (5), Fornals (5), Antonio (7).
Tottenham: Gazzaniga (6), Davies (5), Aurier (6), Sanchez (6), Alderweireld (6), Dier (6), Winks (6), Alli (7), Moura (7), Son (8), Kane (7).
Subs: Rose (6), Sissoko (n/a), Eriksen (n/a).
Man of the match: Heung-Min Son.
How Mourinho survived scare to make winning start
Mourinho said: "My feeling is that we were closer to 4-0 than they were to 3-1 but this is the Premier League. I think my players paid the price for a very difficult week."
West Ham's response, as they had done in their previous home game in the 3-2 reverse to Newcastle, came far too late, and it is now five league defeats in six for Pellegrini. After the whirlwind events of the international break, it is they who desperately need revitalising.
A refreshed Mourinho imbued confidence from the moment he came off the team coach in east London, taking over a team mid-season for the first time since swapping Uniao de Leiria for Porto as a 38-year-old in early 2002.
The Portuguese spoke of needing to "trust the base" he inherited from Mauricio Pochettino - and there was a devastating spell either side of the interval that bore all the hallmarks of his predecessor's side at their swash-buckling best.
Mourinho needed to hit the ground running and, after an opening half an hour low on quality, Dele Alli found the run of Son and he finished low beneath Roberto.
The Spanish goalkeeper had been ironically cheered by his own supporters during an error-strewn first half that got worse for the hosts when Alli was the architect once more for Spurs' second.
Jose Mourinho named both Eric Dier and Lucas Moura in his first Tottenham side. There were three changes from Mauricio Pochettino's last game in charge, with Giovani Lo Celso on the bench and Tanguy Ndombele out injured as Harry Winks was handed a start.
Angelo Ogbonna returned to the West Ham side after being dropped for the last three games while Andriy Yarmolenko returned and Roberto kept his place in goal.
A month can be a very long time in football and, having responded well to his critics in his last away league game at Everton, Alli showed immense dexterity in keeping the ball in play to release Son.
The South Korean spotted the run of Moura at the far post, with the Brazilian getting in front of Aaron Cresswell to blast home his third goal of the season.
Mourinho pointed passionately towards Alli for his role in the goal, but not even the half-time whistle could stem the tide for the beleaguered hosts as Kane was soon celebrating his customary goal in a London derby.
Ogbonna was no match for the England captain as he rose to head in Serge Aurier's pinpoint cross. It was Kane's eighth goal in his last nine Premier League games against West Ham, and his 29th in 46 Premier League London derbies.
The game appeared over as a contest, but by the end it emulated Pochettino's reign in microcosm, serving as a reminder of the work ahead for Mourinho.
Antonio began the unlikeliest of comebacks when he allowed Mark Noble's pass to run across his body, losing Toby Alderweireld to strike beyond Paulo Gazzaniga.
West Ham were denied a second when Declan Rice's close-range finish from Sebastien Haller's knock-down was ruled out by VAR Andre Marriner.
The Hammers did find a second in the final minute of stoppage time when Ogbonna headed in Robert Snodgrass' corner - but it would not deny Mourinho victory on his return to management.
What the managers said
West Ham manager Manuel Pellegrini: "We are playing under big pressure. We know that the derby against Tottenham is a special game, and we wanted to do it better.
"I feel like the team never gave up until the end but we are making too many mistakes without the ball. Every time that we do, we seem to concede."
Tottenham head coach Jose Mourinho: "I belong there [on the touchline]. That is where I belong. That is my natural habitat. I just love it. Especially when things go your way.
"I am not worried about my Tottenham career, I am worried about Tottenham and my players. It was very important. Eleven months without music in the away dressing room. I am very happy for them."
Analysis: Mourinho needs to sort out the defence
Sky Sports' Kaveh Solhekol...
Jose is back and the cameras just can't get enough of him.
The new Spurs head coach was laughing and joking in the tunnel as his players were preparing to come onto the pitch and he was still smiling at the end of the game.
Mourinho waited to congratulate every one of his players before leaving the pitch and there were a few claps for the Spurs fans too.
It's still strange to see Mourinho managing Spurs but we're all going to have to get used to it - especially if his side play like they did for the first hour here.
This Spurs squad looks much stronger than the group of players he had in his final months at Manchester United.
Mauricio Pochettino has left him an incredible legacy - the stadium, the squad and the training ground are all world class. Now Mourinho just needs to sort out the defence - and win a trophy.
Man of the match - Heung-Min Son
Having lost his first competitive game as a manager, with Benfica in September 2000, Mourinho has gone unbeaten in his first game in charge at each of his eight clubs since, winning five - and his latest triumph owed plenty to Son's inimitable energy.
The South Korean is Tottenham's leading goalscorer in all competitions in 2019, netting one more than Kane (19) so far this calendar year, but it was his defensive work during West Ham's recovery that was equally as impressive.
Son regained possession 10 times for his side - only Aurier (13) did so on more occasions, and he was a constant outlet.
Tottenham end away day blues in stats
- Jose Mourinho won as many points today vs West Ham, as Mauricio Pochettino mustered in his final 12 away Premier League games with Tottenham (W0 D3 L9).
- West Ham United have picked up just two points from their last 21 available in the Premier League (W0 D2 L5).
- Tottenham have won three consecutive away league games versus West Ham for the first time in their history.
West Ham travel to face Chelsea next Saturday in the Premier League; kick-off at Stamford Bridge is at 3pm.
Mourinho's first home game as Spurs head coach takes place on Tuesday as Olympiakos visit the Tottenham Hotspur Stadium in the Champions League, while they host Bournemouth back in the Premier League next Saturday at 3pm.