Crawley manager Steve Evans was delighted to beat Torquay 1-0 but admitted he had expected to win.
Matt Tubbs was able to snare the game's solitary goal six minutes before the interval and the winning margin should have been greater.
Torquay goalkeeper Scott Bevan saved second-half penalties from Tubbs and Craig McAllister to keep the game competitive until the death.
However, the game was marred with a dismissal from either side as Chris Zebroski and Dean Howell were sent off.
Crawley have now beaten Torquay, Derby and Swindon in this year's competition.
"We expected to come here and win. We said it and we have done it," said Evans
"Arguably if we go and practise penalties tomorrow we might score the next one.
"I think if the first one goes in then I think we may have won here rather comfortably this afternoon.
"It's fantastic for the owners that we are through to the last 16 for the first time.
"Obviously by progressing in the FA Cup we might encounter some fixture congestion ahead - and now we might do some transfer business before the window closes that wasn't planned.
"I think you have to give us a lot of credit for the way we played today. I have asked them to enjoy every cup day that we have had and that won't change."
Torquay boss Paul Buckle added: "We are disappointed. It's never easy when you lose a game.
"It was a big game today. It was a big game for both sides. We weren't at our best; I'll hold my hands up and say that although it was an unbelievable game with all the incidents in the game, especially the second half.
"We have had lots of good days at Plainmoor but today is not a good day for us. We weren't at our best."
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