A strong West Ham side took advantage of a rare, poor defensive performance by Forest, to take all three points.
In spite of playing some good football in the first half hour, Forest found themselves three goals down and by half time it could have been five for a West Ham side that threatened going forward and defended strongly.
When Forest got a goal back in the second half it looked like there may have been a chance for them to get back into the game, but a fourth goal from West Ham put it out of their reach.
It was a tentative start to the game, lacking in fluency and without much quality into the forward players from either team.
Forest's first real chance came in the 12th minute when the ball came in from Lewis McGugan's corner. Robbie Findley did well to run onto it but the ball came off his shoulder and off target.
Superb build-up play gave Forest another chance and McGugan did all the work to get past the West Ham defence but sent the ball over the crossbar.
Forest came close to taking the lead from a free kick in the 19th minute. Chris Cohen took it 20 yards out on the right and sent a powerful ball towards the back post, forcing a good save from Robert Green, who put the ball round for a corner.
But West Ham were quick on the break and took the lead when Matt Taylor fizzed in a low ball from the left of the box and it went into the back of the net off Luke Chambers, for an own goal.
And they were two up three minutes later from the corner. The ball went high across the box to James Tomkins nodded it back onto the head of Kevin Nolan who headed it in from close range.
Forest reacted well and came close when a superb ball from Radi Majewski found Miller as he raced into the box but, shooting with his left foot, he found the side netting.
Then McGugan forced a great save from Robert Green. Chris Gunter's cross fell nicely for McGugan but the ball came off the post before the keeper made it safe.
West Ham also came close when Julien Faubert's effort took a deflection of Chambers but went wide of the post.
Carlton Cole made it three for the Hammers when the ball came into the box from Joey O'Brien. Winston Reid headed it on to Carlton Cole who rose up and nodded the ball down past Lee Camp.
And they could have made it four when Cole ran clear and Camp didn't commit himself soon enough, allowing Cole to put the ball past him, but Wes Morgan did well to clear the danger.
And West Ham again had too much space in front of the Forest goal when Cole sent the ball across the six-yard box to Nolan who was in too much space, but sent the ball wide of the far post.
Forest had a chance to get one back just before half time when Majewski made the run from midfield and fed the ball through to Miller as he ran into the box and with just the keeper to beat he sent the ball just over the bar.
Forest pushed forward well early in the second half but, with West Ham defending effectively in numbers, they were unable to get anything on target.
Twelve minutes into the half Boateng was replaced by Joel Lynch, with Cohen moving into midfield.
With Forest still not responding, Matt Derbyshire and Andy Reid came on in the 64th minute to replace Majewski and McGugan.
Forest got a goal back with 20 minutes to go when Cohen and Lynch combined well on the left. Lynch fired the ball across the box towards the far post where Findley headed it home.
Forest suddenly looked more lively and the noise around the City Ground swelled to get behind the home side.
But it was the away side that scored when Forest failed to clear a corner and Winston Reid found himself in loads of space to put the ball away from near the back post.
In spite of never giving up, Forest never looked like scoring and it was West Ham who came closest in the third minute of stoppage time when Nolan's shot was only just deflected wide off Morgan.
Just before the final whistle Findley got behind the West Ham and beat the keeper but Tomkins calmly cleared the ball off the line.
Forest: Camp, Cohen, Morgan, Chambers(C), Gunter, Majewski(Derbyshire 64min), Greening, Boateng(Lynch 58min), McGugan(Reid, 64min), Findley, Miller
Subs not used: Smith, Garner
Bookings: Boateng 38min, A Reid 89min,
Scorer: Findley 70min
West Ham: Green, O'Brien, McCartney, Tomkins, Reid, Noble, Collison(Faye 75min), Nolan, Taylor, Faubert, Cole(Piquionne, 68min)
Subs not used: Boffin, Stanislas, Carew
Bookings: Nolan 72min, Faubert 89min
Scorers: Chambers og 21min, Nolan 25min, Cole 32min,W Reid 77min
Referee: G Salisbury
Attendance: 21,379 Away attn: 2,690