Billy McKay and substitute Blair Spittal netted after half-time as County won 4-0 at Brechin to cement their place at the top of Group B.
Brechin boss Barry Smith was back in the dugout after being forced to come out of retirement at the age of 45 for Saturday's 3-0 defeat by Forfar. His side had four more players available to allow him to name a 15-man squad with Luke Watt and Christopher McLaughlin making debuts.
On-loan Norwich midfielder Simon Power twice got inside the home defence in the early stages but could not make the most of his chances and McKay had a shot cleared off the line by Scott Reekie.
The breakthrough came in the 33rd minute when Stewart chested down Joe Chalmers' corner to lash the ball in off the bar from 16 yards.
Stewart had netted a double in Saturday's 4-1 win over Montrose and he emulated that feat with a minute left of the half with a smart finish after some sharp passing.
The striker came close to a hat-trick inside three minutes of the restart following Iain Vigurs' through pass but McKay slid in from close range to make sure his shot crossed the line as Dougie Hill attempted to clear.
Harry Paton sent Spittal clear over the top on the counter-attack to net in the 75th minute.
Matthew Knox missed a glorious chance for a consolation before Hill had a goal disallowed for a foul on goalkeeper Ross Laidlaw as he headed home from close range.