Defensive injury concerns meant the Bluebirds were without a recognised centre-back in their starting line-up, forcing full-backs Perry Ng and Joel Bagan to fill in.
Cardiff’s patched-up defence was put under early pressure from a Derby attack without the injured Sammie Szmodics, and Bagan was forced to clear off the line inside three minutes.
But it was the Bluebirds who took the lead against the run of play when Ashford slotted past Monza-linked Rams keeper Jacob Widell Zetterström.
Cardiff’s lead did not last long. Morris, the Rams’ top goalscorer last season, raced onto a long ball and overpowered Ng before drawing the hosts within seven minutes.
The visitors were back in front before the break thanks to Salech, who made no mistake to score his third of the campaign after being teed up by a selfless Rubin Colwill.
Undeterred, Derby responded once again and levelled for a second time within three minutes of the restart through a thunderous Clark effort from the edge of the box.