This game was not immune to the weather chaos that wreaked havoc with the day's card and kick-off was delayed by 15 minutes as thick fog descended on Dens Park.
That did not unsettle the visitors, who scored after just two minutes with Cadden finishing coolly after a great ball in from the left by Obita.
Obita went from hero to villain soon after and, with the numerical advantage, Dundee were soon back level, McGhee sweeping into the net after a flowing move.
They took the lead on the half hour, Portales seeing his near-post flick deflected into the net by unfortunate Hibs midfielder Triantis.
A calamitous opening 45 minutes for Gray's side was summed up in first-half added time as Dundee extended their lead - Hibs keeper Josef Bursik took a poor touch that was seized upon by Palmer-Houlden, who tapped in.
The second half was a less frantic affair. Hibs had a few chances - Joe Newell and Elie Youan going close - while Palmer-Holden and Lyall Cameron did likewise for Dundee.
And, deep into added time, Main rubbed salt in Hibernian wounds with the fourth.