Hartlepool showed the best early endeavour and struck the woodwork when Gary Liddle blasted in a cross from the right which hit the near post.
The home side had a strong appeal for a penalty turned down by referee Kevin Friend when defender Nathan Smith appeared to use his hand before clearing a Matty Robson cross.
Robson and Kevin Kyle both had free-kicks well saved by Yeovil goalkeeper Josh Wagenaar at the start of the second half, and he also did well to save a Liddle shot at the second attempt.
Yeovil went close when full-back Smith broke down the left and saw his looping shot come back off the underside of the crossbar before Hartlepool cleared.
But the best chance of the game fell to Brown in the 75th minute who could only head the ball straight at goalkeeper Jan Budtz when well placed.