The veteran Belgian stuck both spot-kicks into the bottom left corner before Adil Chihi pulled one back for Cologne before half-time.
Nurnberg had Tomas Pekhart sent off for a second yellow card three minutes before the break, but the hosts could not take advantage and Miso Brecko's dismissal 15 minutes from time evened up the numbers.
Nurnberg started brightly and Markus Mendler picked out Pekhart, who fired a shot against the bar.
They were awarded a penalty in the 31st minute when Pedro Geromel fouled Markus Feulner and Simons slotted home from the spot.
Geromel was having an afternoon to forget and his foul on Pekhart four minutes later gave Simons the opportunity to double the visitors' lead.
Chihi halved the deficit in the 39th minute when he pounced after goalkeeper Alexander Stephan had blocked Lukas Podolski's shot.
And the hosts received another boost when Pekhart picked up a harsh second yellow card for a foul on Geromel.
Despite being a man down, it was Nurnberg who looked the more dangerous and Cologne keeper Michael Rensing had to be alert to keep out Christian Eigler's low shot.
Alexander Esswein was next to test the former Bayern Munich keeper, who was equal to his effort from 18 yards.
But Cologne's hopes receded further when Brecko was dismissed in another harsh decision, receiving a straight red for a challenge on Feulner.
Christian Clemens fired wide as Cologne desperately sought an equaliser, but one never looked like coming.