Crewe needed a win to stand any chance of staying up and Shaun Miller and Gylfi Sigurdsson missed good chances to improve their goal difference.
Steve Collis looked shaky in the Alex goal, twice spilling efforts from Michael Morrison and Steve Howard before the ball was cleared to safety.
Any hopes of Crewe pulling off the great escape were ended by a three-goal salvo started by Berner’s 30-yard side-footed strike 10 minutes into the second period.
Ten minutes later Dyer poked the ball home to make it two.
Then Fryatt, the Foxes’ leading scorer, tucked a perfect finish under Collis to notch his 32nd goal of the season with 65 minutes on the clock.