King header seals Foxes victory
City took the lead after 15 minutes when Lloyd Dyer slipped the ball inside to Matty Fryatt, who scored with a well-placed shot into the top corner of the net from 16 yards.
Crewe keeper Stuart Tomlinson then kept his side in the game with a series of brilliant saves before the Railwaymen conjured up a shock equaliser.
Michael Morrison hesitated after DJ Campbell had failed to clear, allowing Calvin Zola to steal in and fire home an angled shot from 10 yards on the half hour mark.
Leicester struggled to rediscover their fluency after the break, and had to rely on a winner from midfielder King, who rose above a static Crewe defence after 72 minutes to head home substitute Max Gradel’s corner.