Eddie Nketiah started from the bench again having scored the opening goal in the Whites 2-0 win at Barnsley last weekend.
The hosts took the lead in the 20th minute, but it came courtesy of Derby’s Max Lowe putting the ball into his own net.
Marcelo Bielsa’s men had the chance to forge ahead, but Mateusz Klich – who scored from the penalty spot last time out, failed to convert this time.
It looked like Leeds would hang on for a slim victory, until Chris Martin equalised for the visitors in injury time.
Nketiah was introduced in the 79th minute for Patrick Bamford, and within the 11 minutes he featured, the 20-year old made six passes, with an accuracy of 66.7%, also making seven touches.
79' Elland Road rises to applaud Patrick Bamford as he leaves the field, before "Eddie, Eddie, Eddie" resonates around the stadium. 1-0— Leeds United (@LUFC) September 21, 2019
The Anglo-Ghanaian – on loan from Arsenal, is yet to start a match in the English second-tier this term but has played five times off the bench, scoring two goals and providing one assist.
With Leeds not participating in the League Cup third round coming up in midweek, having crashed out in the previous round on penalties to Stoke City, their next game is an away Championship tie at Charlton Athletic next Saturday.