Gareth Allen's side almost took the lead after just three minutes when Jack Lawton hit the bar after great work by Michael Alexander and Adam Bell.
However, Bohemians' best chance of the game came less than 30 seconds later when the ball was cros
sed along the six-yard box but no Gosforth player gambled and the opportunity went begging.
United took the lead when goalkeeper Newbrook's long free kick found Lawton, who controlled well, turned and volleyed past the keeper.
Three minutes later Gary Errington's long free kick was misjudged by the keeper, and while Gary Spottiswood appeared to head home, it later emerged that he hadn't touched the ball and the goal was Errington's.
The second half took a while to get going, and as the pitch cut up the football being played became less attractive.
Tijan Kah had the best chance with a great break, beating two defenders with his pace, but the ball bobbled just before he went to strike it and the keeper made a good save at his feet.
Bohemians' only other chance was a 25-yard free-kick which keeper Newbrook made a decent save from.
