The visitors survived several shaky moments in the closing stages but they held on to leap-frog Hibernian who stumbled to a shock home defeat by Inverness.
Without a victory for five weeks, Kilmarnock stormed out of the blocks and got the all-important goal within 240 seconds.
Rory McKenzie picked up the ball in midfield and supplied the pass to Fowler and the 32-year-old defender curled in a stunner from 20 yards.
Fourth-placed County were shell-shocked and had a smart chance to level on the half-hour but skipper Richard Brittain was wasteful after great support play from Sam Morrow.
Brittain had a great chance to make amends before the break, only to find keeper Cammy Bell in top form who tipped away the midfielder's ferocious drive.
Kilmarnock were very much on the back foot and their cause was certainly not helped just before the interval when winger James Dayton departed the Victoria Park pitch on a stretcher.
Bell continued his heroics in goal in the second half as he kept out again an effort by striker Morrow.
County poured forward in desperate search of the equaliser and Morrow was hugely unlucky in the final minutes when his shock crashed off the post.
Mark O'Hara impressed at the back to deny Steffan Wohlfarth and Evangelous Ikonomous wasted yet another chance with the Greek defender fluffing his shot from close range.
But it was Killie who battled to the spoils as their hopes to finish in the top six received a huge boost.