The high-flying Owls appeared on course to secure a first win at the home of their opponent since April 2007 when they led at the break thanks to Julian Borner's first goal for the club.
The defender cleverly deflected home an on-target shot from Kadeem Harris, who also hit the crossbar as the visitors dominated in the opening half, helped by Australia star Massimo Luongo.
Wednesday might have gone top of the Championship table had it converted its chances and won by more than two goals.
However, in a game played out in heavy rain, Neil Warnock's Bluebirds were far brighter after the interval, substitute Tomlin eventually equalising when he curled home a late set-piece opportunity.
Wednesday would have moved level on points with West Bromwich Albion and Nottingham Forest at the top of the Championship with a 1-0 victory, but needed a smart stoppage-time save from goalkeeper Cameron Dawson to hold on for a point on its travels.