Alistair Roy missed a good chance to give the hosts the lead early on, pulling his shot wide.
Jonathan Page tested Shire's Richard Barnard with a close-range header and nodded another effort over.
Kinnaird fired in what proved to be the winner after increased pressure from the home side in the second half.
Lloyd Kinnaird's second-half strike helped East Stirlingshire defeat East Fife on the opening day of the Scottish League Two season.