The Staggies were the dominant side from the off and, while the Wasps showed commendable resilience, they could have few complaints after goals from Callum Morris and Harry Paton settled the tie.
Alloa had to wait until the 51st minute for their first genuine chance of the match, summer signing Alan Trouten finding space on the edge of the box only to pull his shot just wide of the post.
The Highlanders eventually broke the deadlock on 59 minutes, when Josh Mullin’s goal-bound effort was flicked home by fellow new arrival Morris.
The Staggies made sure of victory two minutes into stoppage time when home keeper Neil Parry could only push Billy McKay’s effort into the path of substitute Paton and the midfielder stroked home his first goal for the club.
While County will learn their opponents in the last 16 later today, Alloa will be gunning for revenge when they head to Dingwall for their Championship opener next Saturday.