Cedwyn Scott was on target to secure the win for Notts at the Jakemans Community Stadium.
A crowd of 1,042 witnessed a very quiet first half, which despite the Magpies dominance provided few goal scoring opportunities.
Aaron Nemane and Jodi Jones with the only real chances for Notts with Boston's keeper Gregory equal to Nemanes near post effort and Jones managing to hit the side netting from a free kick.
A defensive block from Kyle Cameron was enough to snuff out the only real first half chance for the home side.
Notts were unchanged at the restart but Jodi Jones and Tobi Adebayo-Rowling made way for Dan Crowley and Geraldo Bajrami on 55 minutes.
Crowley made his presence known shortly after coming on sending a volley over the top from an O'Brien cross.
O'Brien was involved again shortly after when his cross found Cedwyn Scott who scored with a neat finish on 68 minutes.
Several changes were made on 76 minutes by Luke Williams to see out the remainder of the game including Macaulay Langstaff who had a great chance to double the lead late on but was unable to take his opportunity one on one with the Boston Keeper.
Notts: Stone - Chicksen (Mahovo 76'), Cameron (Cisse 76'), Rawlinson (Brindley 76'), Adebayo-Rowling (Bajrami 55') - Palmer (Bostock 76'), O'Brien (McGregor 76'), Austin (McGoldrick 76'); Jones (Crowley 55'), Nemane (Munakandafa 76'); Scott (Langstaff 76')
Unused: Trialist (GK)