A Jordan Brown shot from distance was the game’s first real opportunity, with Brad Collins collecting the effort comfortably enough.
This was followed by a couple of other dangerous moments, including an Ashley Fletcher header - which was also dealt with by the Brewers shot stopper.
Following the restart, the first real chance fell to Kyran Lofthouse - who could only produce a tame shot to test Franco Ravizzoli.
The next real chance only came in the 90th minute, as Hamilton clinched the win.
On the break, Leighton Clarkson, slipped the winger through down the right, with his shot beating Collins at the front post.
Here’s how the Seasiders performed:
7. George Honeyman - 7
George Honeyman worked hard in the centre of the park throughout. Photo: Gareth Evans
8. Jordan Brown - 7
Jordan Brown tested Brad Collins in the first half with a shot from distance. Photo: Gareth Evans
9. Joel Randall - 6
Joel Randall was once again kept quiet at Bloomfield Road. Photo: Gareth Evans
10. CJ Hamilton - 7
CJ Hamilton took the winning opportunity well, beating the keeper at the front post. Photo: Gareth Evans
11. Ashley Fletcher - 6
Ashley Fletcher came close with a headed attempt towards the end of the first half. Photo: Gareth Evans
12. Tom Bloxham - 6
Tom Bloxham was among the Blackpool attacking players to endure a quiet afternoon. Photo: Gareth Evans