We led early through Gareth Bale but as Jussi Jaaskelainen denied us time after time, West Ham hit back to lead 2-1 via Andy Carroll's penalty and Joe Cole's strike just before the hour.
Jaaskelainen thwarted us again until we found an equaliser with 15 minutes remaining as substitute Gylfi Sigurdsson finished from close range.
Jaaskelainen produced two more fine saves as we poured on the pressure and we were finally rewarded in the 90th minute as Gareth let fly in spectacular fashion from 30 yards, the ball arrowing into the top corner to secure the 3-2 win.
Statistics showed 62 per cent possession and 25-8 efforts on goal in our favour as we made it three wins on the trot, stretched our unbeaten run to 11 matches and our current sequence to one defeat in 15 in the Premier League. We also climbed over Chelsea into third place.
"We had so many incentives to win and the players showed that desire through and through," said Andre.
"They kept on fighting – fighting for the equaliser, fighting for the winning goal.
"We could have easily dropped the lines back and tried to hold onto the point, because that’s always a positive result away from home in the Premier League, but the lads wanted more. We kept pushing and we got the reward we deserved by winning the game.
"It was one of those games where the goalkeeper continues to make saves and I felt it was never going to go in. I know the second goal was a rebound, but it was also down to our perseverance to get the scoreline we wanted.
"Not many teams come here and have an easy time, West Ham are a very difficult team to play against. That’s what makes the win even more rewarding."