In truth Hamilton might have scored more on the day, having made chances galore, but Brechin's goalkeeper Craig Nelson provided some semblance of respectability to the score-line..
The Accies went ahead after 14 minutes when Derek Fleming placed a 20-yard free-kick perfectly to beat Nelson in the top right-hand corner.
Although Brechin might have been expected to attack, the game stagnated for the remaining half hour until half-time, leaving the bemused fans wondering at the lack of ambition of the visiting side.
However, within a minute of the second half, Alex Neil had given his side a deserved 2-0 lead. Scott Tunbridge had strolled past a sleeping Brechin defence and might have gone for goal himself, but instead chose to play the ball across goal for Neil to tap home.
From then the visitors had Nelson to thank for keeping the score down, but he was unfortunate to see Pat Keogh pounce on a parry from Mark Gilhaney's long-range effort for Hamilton's third goal of the match.
Tunbridge came close on another two occasions, again defied by Nelson in the 72nd minute and shooting just wide three minutes from full-time.
Brechin made very few chances and in truth never looked like scoring. Their best effort came from Kevin Byers, who shot wide from 20 yards in the 66th minute.
Gerry Britton missed an open goal from just four yards in the 90th minute, but Brechin deserved nothing from this game.