Midfielder Shinnie's first-half header sealed the points with Clark returning to Blues for the first time since being sacked in October.
His old side hammered another nail in the Tangerines' coffin to leave them bottom, 15 points from safety, in the Sky Bet Championship while Blues rose to 13th.
Robert Tesche made his full Blues bow, replacing the banned Stephen Gleeson, while Blackpool handed a debut to Bournemouth loanee Miles Addison.
Jamie O'Hara fired two efforts straight at Darren Randolph in a scrappy, low-key start before the game settled into a midfield battle until it sprung to life.
Former Aston Villa striker Nathan Delfouneso curled over after 33 minutes and 90 seconds later Blues should have been ahead.
Clayton Donaldson had been quiet but missed a glaring opening when he planted Paul Caddis' wicked cross wide from 10 yards.
However, Blues did take the lead two minutes later when the Blackpool defence went AWOL to Tesche's long ball and Shinnie headed over the advancing Elliott Parish.
It was harsh on Blackpool but their shoddy defending underlined, despite being on top, why they were bottom.
The rest of a poor first half played out without incident and the game restarted in the same vein.
The quiet Demarai Gray shot straight at Parish while Randolph produced a fine stop to deny Gary Madine at point blank range.
The Blues keeper had to once again be alert with 17 minutes left when Tom Barkhuizen skipped through, Randolph blocking the substitute's attempted chip, as Blues held on for the three points
Source : PA