The home side made the brighter start and Luke Murphy saw a side-footed effort deflected over by Joe Edwards, while Yeovil goalkeeper Marek Stech dived low to keep out Chuks Aneke's low drive.
Yeovil had the ball in the net after 20 minutes only for Paddy Madden to be called offside, while Edwards shot over the crossbar from 25 yards.
The visitors were growing in confidence and Edward Upson's teasing shot was only just palmed around the post by Crewe goalkeeper Alan Martin five minutes before the break.
But Martin could do nothing when Webster pounced on a loose ball to drill into the roof of the net from the resulting corner.
Crewe went in hunt of an equaliser and Mathias Pogba shrugged off Yeovil defender Dan Burn, but Stech was equal to his shot and the goalkeeper gathered another effort from Mark Ellis.