The Railwaymen produced their best 45 minutes of football of the whole campaign to leave Russell Slade's Yeovil floundering.
Energetic running from winger Moore and on-loan striker Simon Church was the difference between the sides.
Only Steve Mildenhall in the Glovers goal stood between a more severe beating. The keeper's string of super saves included a first minute block from Gary Roberts, but even he needed help from his woodwork when Ryan Lowe arrowed in a 25-yard free-kick.
Church also headed the rebound on to the bar moments before he was denied by a great save from Mildenhall after he burst through and took aim with his left foot.
It was a momentary reprieve for Yeovil as, from Lowe's in-swinging corner, McCready nudged in front of Lloyd Owusu to head home with help from the striker's arm.
Crewe surged into a two-goal lead five minutes before the interval when Church flew down the left.
The Reading striker, who is on loan at Gresty Road for a month, pulled the ball back across the box and Moore smashed the ball home with the help of a deflection.
Slade made changes for the second half, bringing on strikers James Walker and Wilfried Domoraud, but it didn't improve his side's threat greatly.
It was Crewe who could have added more in the closing minutes with Church shooting inches past the far post and Mildenhall beating out an effort from Moore.
Walker's ambitious overhead flick, which just missed the top corner, was about as good as it got for Yeovil, and their boss Slade admitted afterwards: "It was a bad day at the office for us, but you've got to give Crewe credit as they were very inventive."