Brad Potts came close to equalising four minutes later, but he watched on as his effort came back off the foot of the post.
A glorious chance for the League Two side to double their lead was squandered by Jeff Hughes in the 18th minute, as he swung at fresh air with the goal gaping.
Prince Buaben then saved his team from going two down by clearing Bell's header from a corner off the line.
The teams went in level at the break, but just as the League One side began to grab a toehold they conceded, with Sarcevic lobbing goalkeeper Greg Fleming from just outside the area.
The 21-year-old midfielder had a chance to put the game beyond doubt in the 84th minute, but he sent his shot wide of the post.
However, they still march on to join Rotherham United, Chesterfield and Oldham Athletic in Saturday's draw for the Northern Section semi-finals.