McNulty fired the Rams ahead with a well-taken finish inside the opening 23 minutes, before Riski tapped in at the far post to give Derby a two-goal lead going into the break.
Micky Harcourt curled home a superb free-kick in the 83rd minute to give Matlock some hope, but after a scrappy final few minutes, the Rams held on to seal the win.
The Rams fielded five trialists in the starting line-up, including American duo Danny Barrera and Tom Reilly, with the latter starting at the heart of the Rams’ defence, alongside Stefan Galinski.
Striker McNulty, who is currently plying his trade with Scottish First Division side Livingston, linked up with the Rams earlier this week, and it was the 20-year-old who proved to be a real thorn in the side of the Matlock defence.
Within the space of two minutes, McNulty was denied twice on separate occasions with 20-yard strikes. His first effort came after the 20-year-old nicked the ball off the toes of Laurence Gaughan, before letting fly with a venomous effort that took a deflection on its way to goal as it fizzed narrowly wide.
His second effort came moments later, as in a similar position from the edge of the penalty area, McNulty cut inside and drilled a low strike goal-wards that was clawed behind by goalkeeper Jon Kennedy.
However, it was not all one way traffic as Matlock’s best chance of the half soon followed when a long ball over the top caught the Rams’ defence square. Bradley Grayson ran clear down the right but could only thrash his effort wide of goal.
McNulty might have been thinking it was not going to be his night when he beat three Matlock defenders andd fired a fierce strike that was destined for the bottom corner - only for ‘keeper Kennedy to produce a fine reflex save.
But the Scot did not have to wait much longer for the goal his play deserved, as on 26 minutes McNulty remained cool headed to fire home Josh Lelan’s perfectly weighted cross-field pass.
The Rams continued to dominate, and before the half was up, Finnish trialist Riski doubled the away side’s advantage. Kane Richards’ powerful run down the left was matched by a clever low cross towards the far post, where Riski was on hand to tap the ball in from close-range.
In the second-half Derby continued to dominate as Barrera saw his left-footed strike beaten away at the near post by Kennedy, whilst Riski fired over the crossbar following a mazy run shortly after.
With seven minutes remaining, Harcourt produced a moment of magic for the home side as he bent a 20-yard free-kick round the Derby wall, into the net to halve the deficit. But the Rams stood firm to secure the victory in what was a good workout for the side.
Derby County: Morch (GK) (Deeney 46); Gjokaj, Galinski, Reilly, Lelan (Sharpe 74); Richards, B. Davies (Dales 61), Riski, Barrera; Doyle (Dawkins 61), McNulty (Thomas 74).
Subs Not Used: Naylor.