Well, Mauricio Pochettino will be quite relieved you suspect.
It was a real blow for the Hammers to concede so late in the first half after some resolute defending, and they really had a go in the second half.
But Marko Arnautovic couldn't find a way past Hugo Lloris today. The Spurs goalkeeper produced three excellent saves, which could have been an Arnautovic hat-trick on another day.
It's four successive wins now in the league for Spurs, who climb to third with this result.
You can follow all the reaction to this afternoon's Premier League games over here.
Cheers for joining!
FULL-TIME
West Ham 0-1 Tottenham
And that is it!
Post update
West Ham 0-1 Tottenham
Oh my what a goal that would have been.
Michail Antonio fires the ball from the edge of the area, anticipating the final whistle but the ball rises too high.
That should be that for Spurs, but this second half West Ham showing deserved more really.
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GREAT SAVE!
West Ham 0-1 Tottenham
Lloris has denied Arnautovic AGAIN!
It's another fantastic stop that might just have saved Tottenham the points.
Spurs are hanging on here and the ball keeps coming back at them.
Post update
West Ham 0-1 Tottenham
Offside!
Javier Hernandez has the ball in the back of the net but Arnautovic set off too soon on his run to tee it up.
The joy is short-lived but West Ham continue to drive forward in hunt of a late equaliser.
Post update
West Ham 0-1 Tottenham
The pressure from the home side is mounting now but Tottenham are doing just enough to stay in front.
They've been very good in this second half and you would say on the balance of things a draw would not be unfair between these two.
Spurs haven't been able to give themselves breathing space and they could very well be punished for that.
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SUBSTITUTION
West Ham 0-1 Tottenham
Moussa Dembele returns to action for Tottenham. He's on in place of goalscorer Erik Lamela.
A good showing from Lamela, who has tired slightly in the last few minutes.
YELLOW CARD
West Ham 0-1 Tottenham
Marko Arnautovic earns himself a booking for a poor attempt at a tackle on Kieran Trippier.
Frustration, most likely.
For all their good build-up play, West Ham really haven't created enough in the final third.
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SUBSTITUTION
West Ham 0-1 Tottenham
West Ham call for a penalty, and it's clumsy from Harry Winks but Grady Diangana had already lost his footing.
Michail Antonio is on for Hammers captain Mark Noble with about 20 minutes to go.
Post update
West Ham 0-1 Tottenham
You can tell West Ham believe they can get themselves back on level terms and the crowd are feeding off that.
Tottenham are certainly not in complete control by any means and Mauricio Pochettino will want that second goal as quickly as possible to calm any nerves.
CLOSE!
West Ham 0-1 Tottenham
Hugo Lloris denies Marko Arnautovic again!
Arnautovic doesn't make perfect contact with this one, as he tries to place it into the bottom corner, but the Spurs keeper is able to get a hand to it.
The West Ham forward has a bit of an argument with Davinson Sanchez over a challenge.
There's a bit of fire in this now.
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SUBSTITUTION
West Ham 0-1 Tottenham
Felipe Anderson hasn't been able to have much of an impact on this game and he's replaced by Javier Hernandez.
The Mexico international has missed the last five matches with a virus, so it'll be interesting to see how match-fit he is.
Post update
West Ham 0-1 Tottenham
Lucas Moura is down and has a bit of a cut on his shin following a clash with Robert Snodgrass.
Snodgrass escapes a booking but Moura continues to show the officials the mark left by the Scot. He'll be fine.
Post update
West Ham 0-1 Tottenham
Plenty of energy at the start of this second half with both sides looking dangerous on the break.
Lamela and Moura are offering plenty of pace for Spurs while youngster Grady Diangana is offering a similar threat for the home side.
All in all, it's making for a very entertaining game.
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GREAT SAVE!
West Ham 0-1 Tottenham
That's a fantastic save by Hugo Lloris to keep Spurs ahead.
Marko Arnautovic loops a header towards the top corner but Lloris is able to tip the ball over the bar. One for the cameras.
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Post update
West Ham 0-1 Tottenham
A brief update on Andriy Yarmolenko who went down in the first half - the Ukrainian has been taken to hospital with an ankle injury.
KICK-OFF
West Ham 0-1 Tottenham
The second half begins.
This could still go either way.
Spurs dominate first-half possession
West Ham 0-1 Tottenham
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'Deserved goal for Spurs'
West Ham 0-1 Tottenham
Nigel Reo-Coker
Former West Ham midfielder on BBC Radio 5 live
Finally we've had a goal. Good play, especially from Moussa Sissoko. Great bit of skill and great ball to find Lamela with his left foot.
Tottenham have deserved the lead, they have been the more aggressive of the two sides.
Of all their players Erik Lamela has been the most deserving of a goal, he's looked the bright spark. One of the standout players for Tottenham in this first half.
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'A great bit of skill'
West Ham 0-1 Tottenham
Dion Dublin
Ex-Premier League striker on Final Score
Sometimes you have to
hold your hands up and say it’s a great bit of skill. Moussa Sissoko has got
the cross in and Erik Lamela has ghosted in between two players - bam! It’s a
great goal.
Live Reporting
Harry Poole
All times stated are UK
Get involved
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Getty ImagesCopyright: Getty Images 
Latest PostFULL-TIME
West Ham 0-1 Tottenham
Well, Mauricio Pochettino will be quite relieved you suspect.
It was a real blow for the Hammers to concede so late in the first half after some resolute defending, and they really had a go in the second half.
But Marko Arnautovic couldn't find a way past Hugo Lloris today. The Spurs goalkeeper produced three excellent saves, which could have been an Arnautovic hat-trick on another day.
It's four successive wins now in the league for Spurs, who climb to third with this result.
You can follow all the reaction to this afternoon's Premier League games over here.
Cheers for joining!
FULL-TIME
West Ham 0-1 Tottenham
And that is it!
Post update
West Ham 0-1 Tottenham
Oh my what a goal that would have been.
Michail Antonio fires the ball from the edge of the area, anticipating the final whistle but the ball rises too high.
That should be that for Spurs, but this second half West Ham showing deserved more really.
GREAT SAVE!
West Ham 0-1 Tottenham
Lloris has denied Arnautovic AGAIN!
It's another fantastic stop that might just have saved Tottenham the points.
Spurs are hanging on here and the ball keeps coming back at them.
Post update
West Ham 0-1 Tottenham
Offside!
Javier Hernandez has the ball in the back of the net but Arnautovic set off too soon on his run to tee it up.
The joy is short-lived but West Ham continue to drive forward in hunt of a late equaliser.
Post update
West Ham 0-1 Tottenham
The pressure from the home side is mounting now but Tottenham are doing just enough to stay in front.
They've been very good in this second half and you would say on the balance of things a draw would not be unfair between these two.
Spurs haven't been able to give themselves breathing space and they could very well be punished for that.
SUBSTITUTION
West Ham 0-1 Tottenham
Moussa Dembele returns to action for Tottenham. He's on in place of goalscorer Erik Lamela.
A good showing from Lamela, who has tired slightly in the last few minutes.
YELLOW CARD
West Ham 0-1 Tottenham
Marko Arnautovic earns himself a booking for a poor attempt at a tackle on Kieran Trippier.
Frustration, most likely.
For all their good build-up play, West Ham really haven't created enough in the final third.
SUBSTITUTION
West Ham 0-1 Tottenham
West Ham call for a penalty, and it's clumsy from Harry Winks but Grady Diangana had already lost his footing.
Michail Antonio is on for Hammers captain Mark Noble with about 20 minutes to go.
Post update
West Ham 0-1 Tottenham
You can tell West Ham believe they can get themselves back on level terms and the crowd are feeding off that.
Tottenham are certainly not in complete control by any means and Mauricio Pochettino will want that second goal as quickly as possible to calm any nerves.
CLOSE!
West Ham 0-1 Tottenham
Hugo Lloris denies Marko Arnautovic again!
Arnautovic doesn't make perfect contact with this one, as he tries to place it into the bottom corner, but the Spurs keeper is able to get a hand to it.
The West Ham forward has a bit of an argument with Davinson Sanchez over a challenge.
There's a bit of fire in this now.
SUBSTITUTION
West Ham 0-1 Tottenham
Felipe Anderson hasn't been able to have much of an impact on this game and he's replaced by Javier Hernandez.
The Mexico international has missed the last five matches with a virus, so it'll be interesting to see how match-fit he is.
Post update
West Ham 0-1 Tottenham
Lucas Moura is down and has a bit of a cut on his shin following a clash with Robert Snodgrass.
Snodgrass escapes a booking but Moura continues to show the officials the mark left by the Scot. He'll be fine.
Post update
West Ham 0-1 Tottenham
Plenty of energy at the start of this second half with both sides looking dangerous on the break.
Lamela and Moura are offering plenty of pace for Spurs while youngster Grady Diangana is offering a similar threat for the home side.
All in all, it's making for a very entertaining game.
GREAT SAVE!
West Ham 0-1 Tottenham
That's a fantastic save by Hugo Lloris to keep Spurs ahead.
Marko Arnautovic loops a header towards the top corner but Lloris is able to tip the ball over the bar. One for the cameras.
Post update
West Ham 0-1 Tottenham
A brief update on Andriy Yarmolenko who went down in the first half - the Ukrainian has been taken to hospital with an ankle injury.
KICK-OFF
West Ham 0-1 Tottenham
The second half begins.
This could still go either way.
Spurs dominate first-half possession
West Ham 0-1 Tottenham
'Deserved goal for Spurs'
West Ham 0-1 Tottenham
Nigel Reo-Coker
Former West Ham midfielder on BBC Radio 5 live
Finally we've had a goal. Good play, especially from Moussa Sissoko. Great bit of skill and great ball to find Lamela with his left foot.
Tottenham have deserved the lead, they have been the more aggressive of the two sides.
Of all their players Erik Lamela has been the most deserving of a goal, he's looked the bright spark. One of the standout players for Tottenham in this first half.
'A great bit of skill'
West Ham 0-1 Tottenham
Dion Dublin
Ex-Premier League striker on Final Score
Sometimes you have to hold your hands up and say it’s a great bit of skill. Moussa Sissoko has got the cross in and Erik Lamela has ghosted in between two players - bam! It’s a great goal.