A second-half brace from Rabin Omar, as well as goals from Matt Flynn and Josh Todd, fired home side Annan into the fifth round of the competition for the first time in the club’s history.
An early strike from Matt Flynn gave Jim Chapman’s side a narrow lead and Josh Todd doubled the advantage shortly after the break.
Hamilton’s Greg Docherty pulled one back for the visitors, but the home side responded seconds later as Omar grabbed his first of the game.
Just minutes later and Annan had their fourth when Omar bagged his second of the match, capitalising on yet another defensive error.
The victory was as emphatic as the scoreline suggests, with the League Two side unfortunate not to have scored five or six.
Annan Athletic’s name will be in the hat for the first time as the fifth round draw takes place this evening at 6.15 pm.