Will Hughes nearly opened the scoring with a long-range effort, and the goalkeeper David Marshall came to his side's rescue on a number of occasions.
Jamie Ward went close shortly before the half-hour mark but his strike was well saved by Marshall, before Bryson headed wide on 33 minutes.
However, despite their first-half dominance, the home side found themselves two goals down within 10 minutes of the second period.
Gunnarson turned home an effort shortly after the restart before Whittingham struck a volley to double the lead.
That forced Derby manager Steve McClaren into changes and on-loan Liverpool youngster Ibe arrived off the bench to reduce the deficit just after the hour mark.
Bryson then evened the score up when his fierce effort cannoned in off the post after Marshall had denied another substitute, Johnny Russell, in the build-up.