Richard Batchelor scored the goal in the 20th minute for Leamington's first victory since the opening day of the season.
Rugby Town beat AFC Hayes 4-0 on their own backyard with a brace from Wesley and goals by Hamilton and Steane.
Atherstone Town also won away on Non-League Day with a 2-1 victory at Beaconsfield SYCOB. Smith equalised for the Adders in the 54th minute before Hammersley hit the winner in the third minute of stoppage time.
Bedworth United were also away at Soham Town Rangers and led through a 12th minute Ramsey goal. Ogbonna scored twice for Soham before an Austin own goal two minutes from time gave Beworth a share of the points.
Nuneaton Town drew 2-2 at Worcester City. Lee Moore put Nuneaton ahead in the 32nd minute before Birley equalised three minutes into the second half. Kyle Storer restored Boro's lead in the 57th minute but Mark Danks equalised a minute later.
Iyseden Christie scored for Kettering in a 2-1 home defeat by AFC Wimbledon who top the Conference table.
In the Midland Alliance, Stratford Town beat Friar Lane & Epworth 1-0.
In the FA Vase, Racing Club Warwick lost 6-1 at home to Thurnby Nirvana and Nuneaton Griff lost 2-0 at Goodrich.
In the Midland Combination Premier Division, Alveston were beaten 2-1 at home by Bartley Green, Massey Ferguson lost 6-1 away to Brocton whilst Coventry Copsewood were beaten 1-0 at home to Bolehall Swifts.
In the Presidents Cup, Kenilworth won 2-0 at Northfield.
In the Challenge Urn, Coventry Amatuers drew 4-4 at Lichfield City Reserves but won 3-1 on penalties.