Nuneaton Town are still without a win this season after Saturday's 2-1 Blue Square Bet North defeat at Droylsden.
The visitors had looked on course to pick up three points at the Butcher's Arms thanks to Robbie Burns giving them a first-half lead.
But Boro were undone by a couple of late goals for the Bloods from Danny Rowe and Chris Brown.
The result leaves Nuneaton 19th in the table with just one point from their first three matches.
Tom Berwick scored a hat-trick for Leamington who are now fourth in the Evo-Stik Premier Division thanks to a 4-1 win over Weymouth at the New Windmill.
Bedworth United are top of Division One Central thanks to a third straight win, 3-1 against Fleet Town.
Rugby Town, who also have a 100% record, lie third after a 2-0 win at Burnham.
Stratford Town dumped Nuneaton Griff out of the FA Cup with a 7-0 win in the extra-preliminary round.
Atherstone Town, Studley and Coleshill Town are also through to the next stage of the competiton.
The Adders beat Cadbury Athletic 1-0, Studley won 2-1 at home to Walsall Wood, while Coleshill beat Brocton 5-1.