Newcastle bounced back from last weekend's disappointment at home to Spurs to record their third away win of the season - albeit rather fortunately.
Everton controlled large parts of the match but it was Newcastle's pace on the break that was the Toffees undoing.
A bizarre first goal was gifted to Bellamy after 19 minutes when central defender Abel Xavier collided with goalkeeper Paul Gerrard on the edge of the box.
Another quick break early in the second half saw Gary Speed feed Alan Shearer on the right and his first time cross was met by the head of Nolberto Solano, who placed the ball into the corner of the net.
Everton hit back almost immediately and deservedly scored when David Weir met Niclas Alexandersson's cross.
The goalscoring was wrapped up on 86 minutes when livewire Bellamy broke on the right and crossed for Laurent Robert to feed Clarence Acuna in the box and the Chilean buried his effort.
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