Harding curled a left-footed free-kick over a four-man Leeds wall and into the top-left corner of Casper Ankergren's goal after 18 minutes.
The hosts should have had a second when Ankergren parried a Francis Laurent effort and Hal Robson-Kanu blasted over the crossbar with the goal at his mercy.
Leeds eventually clawed their way back into the game but had a let-off on the stroke of half-time when Lubomir Michalik appeared to push Laurent over but referee Pat Miller dismissed claims for a penalty.
The Whites started the second half more positively and were denied a goal when Adam Federici scooped Neil Kilkenny's 16-yard shot onto the roof of the net.
Both sides created opportunities, with Alex Revell just off target for the Blues, but it was Leeds who pushed hardest for the equaliser, with substitutes Andy Robinson and Robert Snodgrass enjoying the best chances.