The two sides couldn’t be separated in normal time but Amadou Bakayoko inadvertently diverted Kevin Dawson’s bullet header into his own net to give Yeovil the lead.
With nine minutes remaining, Dolan confirmed Yeovil’s progression to the second round with a stunning effort.
The midfielder picked up the ball deep inside his own half, spotted goalkeeper Neil Etheridge off his line, and executed a perfect strike to seal victory for the Glovers.
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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