Christian netted our third goal after a brace from Harry Kane, but we suffered a nervy ending after goals from Javier Hernandez and Cheikhou Kouyate, plus a second yellow card and consequent red for Serge Aurier, allowed the Hammers back into the contest.
Thankfully, we held on at the London Stadium to maintain our 100 per cent away record this season ahead of this week's trips to APOEL in the Champions League and newly-promoted Huddersfield Town in the Premier League.
Here's what the players had to say to us after the game...
On becoming the highest-scoring Dane in Premier League history
"I‘m very happy I’m above Bendtner now, move him aside! If you look at the score we were in complete control and if we’d played the ball even better, we had even more opportunities. Of course, with 10 men it was a different game, they scored and got some confidence back. The timing (of Harry's first goal) was right. As soon as I got the ball I knew we had to go forward. We could have created more but the goal came at the right time for us."
On Serge's dismissal
"It’s always different with 10 men. They feel more confident than when we had 11, it’s harder to press them. We tried, they played longer balls and we didn’t get enough second balls but we held up well. It looks easy when you are 3-0 up but when it’s then 10 men and they score they get the confidence and want to come forward. It was a difficult game and we made it difficult."
On the tense finale
"You can feel the fans, even on the bench, it was nerve-wracking for us as well. The fans were excited at 3-2 and we held on, it’s great to see so many away fans here."
Thoughts on the performance
"I thought we dominated the game and had everything under control. Hugo didn’t have to make one catch until the red card. Then we fought as a team and defended well. It was a good victory, we fought hard for it."
On matching up to West Ham front man Andy Carroll
"We know Carroll is difficult but Jan, Davinson and myself, we made it difficult. It wasn’t the fight we had to win. We had to be high because if you drop thinking you’ll be safe they then drop the ball in the box and it’s difficult. We defended cleverly and, of course, with a red card, they are going to press us. We did well on that point."
On the result
"I said before that game that you get a history with every team so to finally get one over them after the last two seasons is great for us. They’ve put a dent in us two years in a row so to come here and win was huge. We’ve won three out of three now away in the Premier League and it’s really important we keep that run going and try to build a run at home as well."
On the second half
"When we were 3-0 up we were in complete control. I thought we were playing really well. Obviously, as happens all the time in the Premier League, things change really quickly. After the sending-off it became a real battle just to get the three points. It was a hectic last 20 minutes but we did really well to get through it."
On the pattern of the game
"It's always a tough place to come and a great derby for us, the fans and the club so it feels great to win. Of course, we were under pressure at the end but that's football and we managed to grind it out and get a big three points. We were controlling the ball, had a couple of chances, I hit the post and it looked like we were going to see the game out well but goals change games, they got back to 3-1, we then got a man sent off and the game completed changed. We just ground it out. They got back to 3-2 but other than that they didn't create too many chances. It was a fantastic result."
On what was said at the interval
"We were well in control at half-time and we said we'd come out, try to get the third goal and kill the game. In fairness, we got the third but goals change games and whenever you give a team in the Premier League a sniff of a comeback they will try to take it, especially in a London derby. It's all part of the game and we dealt with it well."