Kevin Wilkin's side who top the Conference North table, gave a full start for Cyrus Christie and the loanee from Coventry City's Academy put through his own net in the 38th minute.
Johnson put the visitors 2-0 up in the 66th minute and although Armson pulled a goal back for Boro two minutes later, Nuneaton went down to a defeat.
Nuneaton lead the Conference North table by two points from Guiseley who beat Hinckley United 3-2.
Leamington had one of their lowest crowds of the season when only 275 fans turned up to see The Brakes beat Cirencester Town 1-0 with a 63rd minute goal from Rowe.
Rugby Town won 4-3 at Ashford Town (Middlesex). A brace from Fagin and one from Parsons had VS 3-0 up in twelve minutes. A goal from Rankin and a second half brace from Kiffin tied the game before Keen hit the winner for Rugby in stoppage time.
Atherstone Town lost 3-1 at Daventry Town. King scored a consolation goal for Adders in second half stoppage time.
Coventry Sphinx's Midland Alliance game at Friar Lane & Epworth was postponed.
In the Coventry Charity Cup, the Kenilworth Town V Massey Ferguson Third Round game was postponed.
Alveston lost 2-1 at home to Continental Star in a Birmingham Midweek Floodlit Cup tie.