The game in the East Midlands was the first between the Rams and Pompey since they came up together from League One last season, with Portsmouth winning the title and Derby finishing as runners-up.
And while Pompey's return to the second tier got off to a slow start, spending three of the first four months of the season in the relegation places, their draw with Norwich on Tuesday moved them one place clear of the drop zone.
Derby, by contrast, started the campaign solidly but had struggled in recent weeks.
Having picked up just nine points from a possible 33 in the 11 games since mid-October, Rams boss Paul Warne spoke about being "well aware of the enormity" of their meeting with a side that started the night just four points and four places below them in the table.
After setting his team up to try and smother and frustrate Leeds and Burnley on the road in the past six days, Warne went with a more attacking formation with four at the back while also shuffling his side with five changes.
Two of the five to come into the starting XI for the Rams combined to make a decisive early impression, with winger Mendez-Laing finding Wilson lurking in the box to coolly finish a sweeping move that started with Cashin on the edge of Derby's own area.
Cashin, who was passed fit to play after taking a knock at Turf Moor on Tuesday, got on the end of a Kenzo Goudmijn corner for Derby's second before a smart backheel pass from Mendez-Laing helped set the Rams up for another soon after.
The pass found Craig Forsyth overlapping in the area, and the full-back's low cross was forced home by Adams, via a big deflection, as Derby scored three goals in the first half of a game for the first time since October 2023.
Apart from a cross-turned-shot from Jacob Murphy, which forced Jacob Widell Zetterstrom into action, Portsmouth failed to trouble their hosts.
Derby could have been even better off before half-time if not for a fine save from Nicolas Schmid to deny Jerry Yates.
Pompey's night in the East Midlands only got more miserable after the interval, with the energetic Harness rattling the visitors' defence as he burst into the box before drilling a low ball into the path of backtracking defender Pack, who could only thump it into his own net.
James Collins came off the bench to head just wide in search of a fifth for Derby, while Schmid went on to claw the ball off the line late on to ensure a defensive mix-up did not result in backpass from Abdoulaye Kamara dribbling into his own net.
Derby climb to 14th in the table, seven points clear of the drop zone, while Portsmouth are only out of the bottom three by virtue of having scored more goals than Cardiff.