Clarke could only divert Leon McSweeney's shot past goalkeeper Alex Smithies in the dying seconds to deny Terriers manager Lee Clarke his first away win in charge.
Clarke's men turned in a strong first-half performance and were deservedly in front at the break.
Defender Clarke powered a header against the base of a Stockport post before the Terriers went in front in the 16th minute as Lukas Jutkiewicz's cross found Michael Collins and the Town midfielder fired home from an angle.
Stockport old boy Anthony Pilkington twice went close to doubling the visitors' lead before Stockport hit back with Tommy Rowe screwing a shot wide from 15 yards.
The second half was a frantic affair - Stockport's Chris O'Grady and Matty Mainwaring both testing 'keeper Smithies, while at the other end Gary Roberts and Pilkington came close to doubling the visitors' lead before Clarke's late blunder.