The Cottagers midfielder netted either side of the break and although Richard Garcia reduced the arrears late on, Hammers eventually paid dearly for their lack of penetration in front of goal.
A strong Fulham side contained recovering car crash victim Chris Coleman, Jon Harley, Barry Hayles, Luis Boa Morte and former Chelsea regular Goldbaek, and they certainly started the more menacing against a West Ham side also boasting a sprinkling of players with first team experience.
After 15 minutes, Boa Morte's low 25-yard free-kick thudded off the base of David Forde's left hand upright and across the face of goal.
At the other end, a quick Hammers break climaxed with the lively Laurent Courtois drilling an angled shot agonisingly past the far post before another Cottagers attack saw Elvis Hammond fire Hayles' nod down just wide to leave the hosts' defence All Shook Up.
As the half hour mark approached, the pace of Riza got the better of an advancing Marcus Hahneann, but after emerging from his tackle with the Fulham keeper in possession of the ball, the Hammers striker could only steer his 15-yarder into the side-netting.
On 33 minutes, however, Fulham finally breached the Hammers defence containing Steve Potts, Scott Minto and Ragnvald Soma when Goldbaek's low 25-yard free-kick sizzled past the West Ham wall before taking a deflection on it's way into the bottom left hand corner.
As the interval neared, both the breaking Titi Camara and then the luckless Omer Riza failed to take advantage when sent clear with just Hahneann to beat.
A lively start to the second period saw both Michael Timlin and Riza booked for tenacious challenges, while Anton Ferdinand, Garcia and Riza each sliced wide.
With West Ham now looking far more urgent, Garcia then forced the Fulham keeper into a full length save with an 18-yard screamer.
Sadly it was to prove a false dawn, for on the hour the classy Goldbaek strode down the right flank before nonchalantly sending an inch-perfect chip over the stranded Forde from 12 yards to double the west Londoners' lead.
But 10 minutes later, West Ham gave themselves hope when Riza invited Garcia to gallop through the heart of the Fulham defence and slot past the exposed Hahneann from 12 yards out.
In injury time, Riza again found himself in the area with just Hahneann to beat, but his and Hammers' evening was summed up when he was muscled out by a pack of retreating defenders.
Team: Forde, Potts, Minto, Garcia, Iriekpen, Soma, Ferdinand (Allen 62), Ferrante, Riza, Camara, Courtois. Subs unused: Jackson, Mehmet, Ward, Lumsden.