Before kick-off the crowd paid tribute to 14-year-old Pompey supporter Beau Croucher who died last month after being hit by a bus.
Earlier on Tuesday it was also announced that club legend Alan Knight had died aged 65 after being diagnosed with prostate cancer in 2024.
Tributes will be paid to Knight on Saturday.
On the pitch the Rams snuck themselves into the lead after 16 minutes when Bobby Clark broke down the right and pulled the ball back into the box for Szmodics.
The forward spun and managed to squeeze the ball in, aided by a couple of deflections.
Pompey’s Abu Kamara wanted a penalty after 30 minutes as he broke into space down the right and went down in the box, but referee Sam Allison waved away claims for a spot kick.
The hosts came close to equalising early in the second half – Zak Swanson swung a cross into the box that ended up having to be diverted behind via the upright by Jacob Widell Zetterstrom.
The resulting corner was cleared only as far as Kamara who sent a powerful shot towards goal but it was deflected narrowly wide.
Derby doubled their lead after 60 minutes as Oscar Fraulo found substitute Salvesen who took a touch that lofted the ball into the air and fired the effort home on the volley into the top left-hand corner.
Portsmouth have the chance to pick up their first home points of the season on Saturday when they face Cardiff, while John Eustace’s Rams go to West Ham.