The 19-year-old, who entered the fray as a second-half substitute, marked his bow in English football by firing a shot into the roof of the net in the 87th minute to send Steve McClaren’s men through.
Both teams made six changes, with Derby giving loan signing Ryan Shotton his debut, and after a quiet opening half-hour the home side could have scored twice in the space of a minute.
Leon Best had a shot from the edge of the box turned behind by Nick Pope in the 33rd minute and Jeff Hendrick scuffed wide from 10 yards 60 seconds later.
Derby ended the first half strongly and they started the second confidently with Best going close before Simon Dawkins just failed to connect with a Johnny Russell cross on the hour.
Charlton had defended well but Derby got the goal their pressure deserved three minutes from the end when Chris Martin made a strong run into the box before setting up Calero who lashed a shot past Pope from 12 yards.