Nicky Maynard's brace secured three potentially vital points for Crewe in their battle against relegation.
Maynard's first goal was a drive off the post and he doubled his tally after the break with a calm 25-yard lob.
The home side thought a Terry Skiverton header was deflected over the line late in the game via Lloyd Owusu and the crossbar, but the goal was not given.
Tom Pope tapped in Crewe's third in injury time with Yeovil down to 10 men after Owusu had to be stretchered off.
Yeovil Town manager Russell Slade told BBC Somerset:
"We had a good deal of possession but couldn't turn it into goals and to be honest I thought we wasted a lot of good opportunities in and around the box in the first period.
"Not much was going our way, that's probably summed up by a ball that my skipper swears was two foot over the line but there you go, that's life at the minute.
"What we didn't need was to concede a goal in the second period and to do that then was criminal really."
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