The England under-21 starlet hit a superb strike in the 49th minute, after Trevor Sinclair had celebrated his return to first team action following his memorable World Cup finals experience with an early equaliser to cancel out Mark Rivers' fifth minute opener.
The scoring was rounded off in the 78th minute by Joe Cole, who fully deserved his first goal of the pre-season campaign following another scintillating all-round display.
In a free-flowing and entertaining game at Carrow Road, Hammers gave an encouraging performance against the side who came within a whisker of reaching the Premiership in May when they lost a thrilling First Division play-off final against Birmingham City on penalties.
Hammers boss Glenn Roeder fielded more or less a full strength side as he welcomed back Sinclair, who settled back into the swing of things straight away following his fantastic performances in the far east.
Also appearing for the first time this summer was young French striker Youssef Sofiane, signed on a free transfer from Auxerre at the end of last season, who came on as a 79th minute substitute for Fredi Kanoute.
New signing Gary Breen wasn't involved, having only completed his first training session with the club earlier in the day, but Christian Dailly returned after missing the clash against Colchester United as Hammers stepped up their preparations.
However, it was Norwich who made the brighter start, taking the lead after just five minutes, when a neat pass found Rivers in the penalty area and the midfielder slotted his shot past David James from 12 yards out.
Just two minutes later, though, Hammers were level. A move that started with a perfectly-timed Tomas Repka tackle on the breaking Nielsen then saw Cole thread an excellent pass through for Kanoute, whose deep cross from the right wing was met at the far post by Sinclair, who thundered his header past Green.
For the rest of the half, it was Cole who once again orchestrated things for the Hammers from the centre of midfield, creating his team's best attacks with an array of dazzling moments, including one simply breathtaking crossfield pass that Kanoute should have converted and another mazy run that almost led to another chance for the Frenchman.
The only other opportunity of any real note in the first half arrived for Norwich just three minutes before the break, when a right wing cross from Rivers was met by Nielsen, whose bullet header appeared to be goalbound until James somehow flung up a hand to tip the ball spectacularly over the bar.
In the second half, it was back to the 'Joe show' as the young midfielder turned on the style with a typically explosive performance.
While these pre-season friendlies against lower opposition hardly offer a sign of things to come once the Premiership campaign kicks off, Cole, in the latest two warm-up matches, has controlled proceedings in such a fashion that can only provide genuine excitement for Hammers fans as the real action approaches.
Just a minute after the interval, his pacy run and slide-rule pass set Defoe in, but a late offside flag thwarted the youngster as he tucked the ball past Green.
However, that only succeeded in giving the goal-hungry 19-year-old the taste for more, and three minutes later his name was predictably on the scoresheet.
A pass out of the Norwich defence accidentally cannoned off referee Danson, and the ball fell kindly for Carrick. He immediately fed Defoe, who turned his marker on the edge of the area and fired a blistering low shot into the corner of the net.
Trevor Sinclair then missed a glorious chance to double his tally, when he rose to meet Richard Garcia's excellent cross but didn't make proper contact and the ball was cleared.
12 minutes from time, Defoe turned provider for Hammers' third and final goal when his lofted pass into the area fell kindly for Cole, who emphatically volleyed past Green from 12 yards out to set the seal on his outstanding performance.
Norwich (4-4-2): Green; Nedergaard (Russell 82), Kenton, Fleming, Drury; Rivers (Notman 63), Mulryne, Holt, Easton (Llewellyn 66); Roberts (Hayes 63), Nielsen (McVeigh 63). Subs unused: Emblem, McGovern, Sutch, Heckingbottom, Crichton (GK), Libbra.
West Ham (4-4-2): James; Schemmel, Repka, Dailly, Winterburn (Courtois 82); Garcia (Moncur 74), Cole, Carrick, Sinclair (Labant 74); Kanoute (Sofiane 79), Defoe (Camara 86). Subs unused: Pearce, Van der Gouw (GK), McCann, Soma, Iriekpen.
Att: 15,913