Alex Meechan's late strike condemned Boston United to defeat in a drab Blue Square Bet North encounter.
Matt Breeze's long-range effort put the visitors in front and Worcester could have gone further in front before the Pilgrims sparked into life.
Newsham hauled the Pilgrims level before half-time, smashing the ball home following a goalmouth scramble.
The game looked to be destined for a draw during a forgettable second half until substitute Kallum Smith had a golden opportunity to put Boston in front. But Smith dragged his effort wide after being set up by Newsham.
It proved to be a key miss as within a minute Meechan showed great composure to fire past Dan Haystead.