The powerful Tynesiders had too much strength for a West Ham side that showed plenty of flair, but were too often muscled off the ball.
A place in the quarter-finals was up for grabs and the Hammers never really got out of the starting blocks as the Geordie boys showed right from the start they were not intimidated by the Cockney crowd.
The home side were rocked on 15 minutes when Newcastle grabbed the lead.
From their first corner, Ryan McGorrigan's delivery saw Filip Modelski block on the near post, but when the ball came out, Jeffrey Henderson thumped it into the net, despite the efforts of a defender on the line.
The goal rocked West Ham and the visitors could easily have added to their tally before the break.
Greg McDermott clipped the crossbar and Bradden Inman headed inches wide, before George Moncur went close for West Ham just before the interval with a rasping drive from 20 yards which flew just wide.
West Ham needed to start well after the break, but it was Newcastle who stepped up a gear to quickly put the game out of the Hammers reach.
On 49 minutes, Philip Airey was put clean through and finished with precision and just three minutes later, Inman thumped home a superb 20-yarder that keeper Loveday could only wave at, as it flew into the corner of the net.