Matt Fryatt struck early on for City who were stunned when Crewe equalised through Calvin Zola before midfielder King conjured up a second-half decider.
City's first chance came on 11 minutes when King burst onto a Matt Oakley throughball before blazing wide from 16 yards.
But there was no mistake about Leicester's opener which came on 15 minutes when Lloyd Dyer played the ball inside to Fryatt who scored with a superbly struck shot into the top corner of the net from 16 yards.
Moments later Crewe keeper Stuart Tomlinson spread himself to deny Dudley Campbell at close range as the Foxes surged forward for a second.
Tomlinson then came to the rescue again when he clawed away Oakley's header before Crewe stunned City with an equaliser on 30 minutes.
Michael Morrison was hesitant after Campbell had failed to clear and Zola stole in to drill home an angled shot from ten yards.
Tomlinson then denied Fryatt and Oakley in quick succession, but it was Crewe that might have snatched a shock lead just before the break when Danny Woodards sent Zola racing clear for a shot on goal but David Martin saved the Foxes when he sprinted from his line to make a vital block.
Leicester struggled to recapture their first-half fluency and had to wait until the 70th minute before producing a worthwhile threat when Tomlinson had to be at full stretch to keep out a Fryatt header.
But King saved City's blushes on 72 minutes when he rose above Crewe's static defence to head home substitute Max-Alain Gradel's corner.