Almost 20,000 were in attendance as the Glovers began the game by testing Black Cats’ keeper Johnny Mapson in the early stages.
The First Division side looked nervy and fell behind as Yeovil’s Alec Stock’s driven effort flew past Mapson.
Jackie Robinson tapped in to level for Sunderland and the tie went to extra-time.
Fog fell over Huish Park but it proved to be a lucky omen for the hosts who progressed the fifth round with Eric Bryant netting a memorable winner.
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Advent Calendar Day One: YTFC’s Number One
Advent Calendar Day Two: Daryl Allinson
Advent Calendar Day Three: YTFC 2-1 Crawley Town
Advent Calendar Day Four: ‘What A Strike!’
Advent Calendar Day Five: A Year In Charge
Advent Calendar Day Six: Nostalgia Mode
Advent Calendar Day Seven: Play-Off Classic