The dismissal of Stewart Greacen proved crucial as Derry blew a two-goal lead in the closing minutes against Cork.
It looked as though two first-half goals from Rory Patterson would help Derry to their first league win in Turner's Cross for 12 years.
Greacen was sent off after an hour for two bookable offences and it was the turning point of the game.
Cork scored twice in the last 10 minutes through Sullivan and Duggan to snatch a draw against the run of play.
Patterson broke the deadlock early with a ninth minute goal.
Stephen McLaughlin slipped him through and the striker made an intelligent run to lose Cork defender Kalen Spillane before slotting the ball underneath the body of goalkeeper Mark McNulty.
It got even better for the visitors when Patterson scored again after 22 minutes.
Ruaidhri Higgins and Owen Morrison were involved in the build-up before Patterson carved out an opening, finishing across the face of goal from an acute angle.
Turner tried to mount an instant response for Cork and forced Gerard Doherty into two saves before the interval.
It remained comfortable for Derry and, after just two away wins in the league this season, they looked on course for a first win in Cork since 2000.
However Greacen's dismissal stirred Cork and they pulled a goal back through Vinny Sullivan on 81 minutes. Shane Duggan grabbed the equalizer five minutes from time.
The draw keeps Derry in fifth place in the premier division.