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Yeovil Town 1-1 Carlisle United (4-5 pens)
Carlisle will host Everton in the FA Cup fourth round after beating League Two rivals Yeovil on penalties.
Mark Ellis scored the crucial spot-kick after Matt Dolan missed.
Jack Compton had given Yeovil the lead in the first half before Anthony Sweeney headed a late equaliser, while Yeovil's Francois Zoko missed a penalty in injury time of normal time.
Yeovil's Alex Lacey saw red for a tackle in extra time before Carlisle's Luke Joyce was also dismissed.
The first eight penalties of the shootout were all scored before Dolan missed when his effort was pushed on to the post by United keeper Mark Gillespie.
Defender Ellis, who was made a permanent signing this month after a loan spell, sealed Carlisle's passage by slotting in the next penalty.
Yeovil should have clinched victory in stoppage time after Gillespie fouled Zoko in the box, but the former Carlisle player fired the resulting spot-kick wide.
The Cumbrians, who are 10th in League Two, will play the Toffees in a live TV broadcast at 13:30 GMT on Sunday, 31 January.
Yeovil manager Darren Way: "They gave everything to the final whistle and it's always cruel when you get knocked out on penalties, but I've got to keep their heads up.
"We've got to deal with adversity this year as to where we are and it's important we stay strong and keep going.
"One thing you'll find is we'll keep pushing and stay positive, no matter what the situation is, because that's part and parcel of football."
Carlisle manager Keith Curle: "It's a good way to win a cup tie for the neutrals. Our thoughts go to Yeovil who put in a very good performance today.
"They looked more dangerous than us at times because we didn't play well today but we knew we needed to have cup tie football and try and frustrate Yeovil.
"We did at times, and you just need a little bit of luck sometimes - and we got that with Francois Zoko missing the penalty."