Match ends, Wolverhampton Wanderers 3(3), Fulham 3(5).
Hugo Rodallega's kick earned Fulham an FA Cup penalty shootout win over Wolves and a fourth-round trip to Sunderland.
On a night tinged with sadness for Wolves following the death of former owner Sir Jack Hayward, Cauley Woodrow headed Kit Symons' side in front.
Dave Edwards and Rajiv van La Parra scored for Wolves before Woodrow forced extra time.
Edwards gave Wolves an extra-time lead, but Ross McCormack's last-minute penalty took the tie to spot kicks.
Fulham converted all five in the shootout to secure a fourth-round trip to Sunderland, as Matt Doherty missed Wolves' second kick.
On a freezing cold night at Molineux, which deteriorated into a fierce snowstorm in extra time, Fulham had the better of the opening half.
They were finally rewarded for their early pressure when Konstantinos Stafylidis sent a left-wing cross into the box that was met by the unmarked Woodrow.
Moussa Dembele could have put the visitors almost out of sight before the break when the Frenchman rounded Carl Ikeme only to miss the target.
|Fulham's third dimension|
|Fulham's penalty shootout win means they retain an unbeaten record in FA Cup third-round ties stretching back to 2008|
Boosted by the double substitution of Edwards and Nouha Dicko, Wolves were transformed after the break.
Dicko was close to giving the hosts the perfect start to the second half but his tightly angled shot hit the side netting.
Wolves twice hit the woodwork through Doherty's header and Dicko's fierce shot before drawing level in the 71st minute.
A clever ball from Dominic Iorfa allowed Edwards clean through to spark a burst of three goals in five minutes.
Van La Parra put Wolves ahead from Kevin McDonald's superb through-ball but Fulham quickly made it level again through Woodrow, who tapped home Dembele's rebound to book an extra half-hour.
McDonald almost put Wolves in front again when he unleashed a shot from long range in extra time which forced Marcus Bettinelli to save.
With snow falling thickly, Edwards put Wolves back in front with a neat near-post finish three minutes into the second half of extra time.
But there was more drama to come in the final minute when Lee Evans handled and McCormack levelled from the spot - before the contest was settled on penalties.
Fulham manager Kit Symons, speaking to BBC London 94.9: "What a way to win a cup tie. It had a bit of everything.
"When Ross McCormack's shot hit the wall, I thought our chance was gone, but I was delighted the penalty was given and he slotted home coolly.
"It was quite an emotional evening for the Wolves fans, who got right behind their team. And rightly so, Sir Jack Hayward is a real loss to the game after all he's done."
Wolves manager Kenny Jackett, speaking to BBC WM: "Fulham played well in the first half and deserved their lead but, in difficult conditions, we got ourselves in pole position and it was a cruel way to lose.
"With their late penalty, I've looked at the video and it's hard to see clearly, but the referee was a lot closer than I was and there's nothing we can do about it.
"It was tough for both sides out there when the snow started coming down, but it was the right decision to continue playing."
- 7HenrySubstituted forEdwardsat 45'minutes
- 17van La ParraBooked at 73mins
- 20McAlindenSubstituted forDickoat 45'minutesSubstituted forClarkeat 118'minutes
- 8ParkerSubstituted forZveroticat 105'minutes
- 32KavanaghSubstituted forRobertsat 78'minutes
- 16WoodrowBooked at 59mins
- 25DembeleSubstituted forRodallegaat 78'minutes
- 44McCormackBooked at 90mins
- David Coote
- Shots on Target
Penalty Shootout ends, Wolverhampton Wanderers 3(3), Fulham 3(5).
Goal! Wolverhampton Wanderers 3(3), Fulham 3(5). Hugo Rodallega (Fulham) converts the penalty with a right footed shot to the top right corner.
Goal! Wolverhampton Wanderers 3(3), Fulham 3(4). Leon Clarke (Wolverhampton Wanderers) converts the penalty with a right footed shot to the bottom right corner.
Goal! Wolverhampton Wanderers 3(2), Fulham 3(4). Patrick Roberts (Fulham) converts the penalty with a left footed shot to the centre of the goal.
Goal! Wolverhampton Wanderers 3(2), Fulham 3(3). Lee Evans (Wolverhampton Wanderers) converts the penalty with a right footed shot to the top left corner.
Goal! Wolverhampton Wanderers 3(1), Fulham 3(3). Konstantinos Stafylidis (Fulham) converts the penalty with a left footed shot to the centre of the goal.
Penalty missed! Bad penalty by Matt Doherty (Wolverhampton Wanderers) right footed shot is close, but misses to the right. Matt Doherty should be disappointed.
Goal! Wolverhampton Wanderers 3(1), Fulham 3(2). Cauley Woodrow (Fulham) converts the penalty with a right footed shot to the bottom left corner.
Goal! Wolverhampton Wanderers 3(1), Fulham 3(1). Dave Edwards (Wolverhampton Wanderers) converts the penalty with a right footed shot to the top left corner.
Goal! Wolverhampton Wanderers 3, Fulham 3(1). Ross McCormack (Fulham) converts the penalty with a right footed shot to the bottom right corner.
Penalty Shootout begins Wolverhampton Wanderers 3, Fulham 3.
Second Half Extra Time ends, Wolverhampton Wanderers 3, Fulham 3.
Goal! Wolverhampton Wanderers 3, Fulham 3. Ross McCormack (Fulham) converts the penalty with a right footed shot to the bottom right corner.
Penalty conceded by Richard Stearman (Wolverhampton Wanderers) with a hand ball in the penalty area.
Attempt blocked. Ross McCormack (Fulham) right footed shot from outside the box is blocked.
Foul by Kevin McDonald (Wolverhampton Wanderers).
Seko Fofana (Fulham) wins a free kick in the defensive half.
Substitution, Wolverhampton Wanderers. Leon Clarke replaces Nouha Dicko.
Foul by Rajiv van La Parra (Wolverhampton Wanderers).