Neil Wood's side, who lost Hannibal to injury just after Neville's 22nd-minute opener, also had a Hugill penalty saved and hit the woodwork with several efforts including a Shoretire free-kick.
The clean sheet is another positive, after recent games that were full of goals at both ends.
The visitors were reduced to ten men after just eight minutes, when centre-back Daniel Oyegoke was sent off for a foul on Hannibal. And although Gunners goalkeeper Arthur Okonkwo saved the resulting penalty taken by Joe Hugill, Neil Wood's team eventually made the extra player count.
Neville calmly converted from Hugill's square pass in the 22nd minute and Shola Shoretire came closest to doubling the first-half lead when his direct free-kick hit the crossbar, while Ethan Galbraith had a similar set piece tipped over by Okonkwo.