Roos was kept busy in the opening exchanges, as he was then called upon to deny Dembele again and then Stephen Arthurworrey.
In the 27th minute, the young forward pounced on Craig Forsyth's dreadful backpass and calmly finished to give the Cottagers the lead.
As half time drew closer, Johnny Russell was handed two chances to restore parity for Derby.
First, he bent his strike narrowly wide after neat work from Simon Dawkins before firing at Kiraly when one-on-one.
The miss proved costly as Dembele doubled the hosts' lead a minute before the break, but Derby were gifted a lifeline in stoppage time as the referee spotted a handball inside the area and Martin halved the deficit with the last kick of the first period.