Hamilton recorded their fourth successive victory and fourth straight clean sheet with a comfortable win.
The home side took a deserved lead as Juanjo volleyed home from close-range after meeting Mark Gilhaney's cross.
The visitors had Daniel Grainger sent off just after the interval following a late lunge on Juanjo.
A minute later, the hosts doubled their lead when Gilhaney headed home James McArthur's cut-back to effectively end the game as a contest.
Hamilton Accies: McEwan, Elebert, Thomson, Fleming, Ferguson (McAlpine 65), McArthur, Neil (Keogh 72), Juanjo, Agnew, Carrigan (Torres 59), Gilhaney. Subs Not Used: Galloway, Jellema.
Goals: Juanjo 36, Gilhaney 52.
Brechin City: Nelson, McEwan, White, Walker, Grainger, Byers, King (Wilson 55), Johnson, Hampshire (Gibson 72), Smith, Burns (Templeman 58). Subs Not Used: Callaghan, Hillcoat.
Sent Off: Grainger (51). Booked: White.
Ref: C Hardy