The visiting side to Meadow Park took an 11th-minute lead through Charles Vernam but Chuba Akpom levelled 10 minutes later.
But Mason Bennett restored Derby’s lead on the stroke of half-time.
This lead was doubled by Alex Babos on the hour.
A second goal in as many matches from Jordi Osei-Tutu gave Arsenal hope of getting something and in the fourth minute of time added on Pleguezuelo, pictured above, stepped up from defence to deliver it.
The point keeps Arsenal in third, while Derby are sixth.
Arsenal: 7 Jan v Liverpool (A) PL2
Derby: 19 Dec v Dinamo Zagreb (A) PL Int Cup