The teacher Danny Carroll scored the two goals that took Farnborough into the fourth round as they handed out some deserved punishment to a poor Darlington side that were well beaten at a snowy Feethams.
Farnborough are the only non-League side definitely through to the fourth round, Carroll hitting the winner after an hour to earn a place in the last 32. "We had to win," the midfielder joked, "or the kids would have made my life hell when I got back to school.
"It's a dream come true and obviously we will be watching the fourth-round draw with more than a little interest now."
However, the Conference side's manager, Graham Westley, bucked the general trend by claiming that he wants another small club in today's draw. "Realistically, a lower League side would probably suit us better than one of the big boys," Westley admitted.
Farnborough made most of the early running and deservedly took the lead in the tenth minute, the top scorer Rocky Baptiste diving to head in a Michael Warner cross.
Only three minutes later the Third Division side equalised. A free-kick was needlessly conceded by the visitors, and Richard Hodgson sent over a pinpoint cross for Ashley Nicholls to head past Farnborough's keeper Tony Pennock.
Warner was again to the fore for the Hampshire side in the 19th minute, sending over another telling cross that Carroll converted. Baptiste then should have made it three in the 21st minute but he fired wide from a good position.
Darlington slowly began to respond and, after several near-misses, their pressure eventually paid off in the 36th minute when striker Ian Clark dived in at the far post to convert a Neil Wainwright cross.
In the second half Farnborough looked happy to hold out for a replay. Yet they stunned their hosts by going ahead again on the hour as Darlington failed to cut out a deep, right-wing cross and Carroll was left totally unmarked at the far post to shoot home.
"It was a job well done," said Westley after his side finally managed to hold on to a lead. "We believed that we could win the game, so we came here to do just that. We had the self-belief to win the game, and we had to adapt to the conditions.
A disappointed Darlington manager Mick Tait was perplexed by his side's showing. "We under-performed. I can't believe that that was one of my teams out there," he said. "We failed to match them in all departments, and ultimately we paid the price."
Goals: Baptiste (10) 0-1; Nicholls (13) 1-1; Carroll (19) 1-2; Clark (37) 2-2; Carroll (60) 2-3.
Darlington (4-4-2): Porter; Valentine, Liddle, Whitehead, Betts; Hodgson (Mellanby, 71), Keltie, Nicholls, Wainwright: Offiong, Clark. Substitutes not used: Pearson, Maddison, Clarke, Collett (gk).
Farnborough Town (4-4-2): Pennock; Warner, Bunce, Laker, Gregory; Butterworth (Annon, 90), Watson, Carroll, Holloway; Charlery (Vansittart, 88), Baptiste. Substitutes not used: Taggart, Green, Benstead (gk).
Referee: G Salisbury (Preston).
Bookings: Darlington: Liddle, Wainwright. Farnborough: Bunce, Holloway.
Man of the match: Carroll.