Armson fired Boro ahead in the 13th minute only for Matt Rhead to level a minute later.
Former Coventry City reserve teamer Donovan Simmonds hit the winner in the 38th minute.
Leamington drew 0-0 at Salisbury City in front of a crowd of 950.
Rugby Town beat Marlow 2-0 in a Southern League Central Division match but Bedworth United lost 3-1 at Beaconsfield SYCOB and Atherstone Town took a 22nd minute lead through Smith but lost 6-1 at Burnham.
Stratford Town drew 2-2 at home to Biddulph Victoria.
Coventry Copsewood are out of the FA Vase with a 3-0 Second Round defeat at Midland Alliance side Westfields.
In the Midland Combination Premier Division, Racing Club Warwick, Massey Ferguson and Nuneaton Griff were all beaten.
In Division One, Kenilworth Town won 3-1 at West Midlands Police.
In Division Two, Young Warriors led 2-1 at Continental Star Reserves only for the match to be abandoned in the 86th minute and Leamington Hibs drew 2-2 at Droitwich Spa Reserves.
In Division Three, Coventry Amateurs lost 4-0 at home to Aston.
Full Coventry Charity Cup details will appear on this site later.