Davies calmly steered the ball down the centre of the goal and past Forest keeper Paul Smith from 15-yards to give the Glovers an emphatic 5-2 victory on the night and a 5-4 aggregate win.
An unfortunate own goal by Alan Wright and a strike from Marcus Stewart in the final eight minutes saw Yeovil level the tie 3-3 on aggregate with a 3-1 win after 90 minutes to force extra-time.
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