Both teams were creating opportunities in what was a relatively open game of football, with Southampton summer signing Mohamed Elyounoussi nearly getting on the scoresheet after strong play from James Ward-Prowse down the right flank.
That let-off was soon capitalised on by Derby, as Lawrence opened the scoring for the Rams after being played through on goal before slotting the ball past McCarthy.
The East Midlands outfit doubled their lead with 19 minutes remaining as Lawrence found the back of the net for the second time, with a low shot being directed into the bottom corner of the net after a direct run.
Frank Lampard's side were continuing to show a desire to score further goals, and the third arrived thanks to Mason Bennett, who tapped home from close range after debutant Florian Jozefzoon had seen a shot parried by McCarthy.
DERBY COUNTY: Carson (Roos 72'), Wisdom (Bogle 72'), Davies (Pearce 72'), Keogh (Hanson 77'), Lowe (Bird 69'), Bryson (Johnson 72'), Ledley (Huddlestone 63'), Mount (Butterfield 77'), Lawrence (Thomas 72'), Nugent (Bennett 72'), Wilson (Jozefzoon 63'),
SOUTHAMPTON: McCarthy, Stephens (Clasie 80'), Hoedt, Targett (Vestergaard 46'), Bertrand (McQueen 80'), Lemina (Gallagher 80'), Ward-Prowse (Hojbjerg 63'), Armstrong (Romeu 63'), Redmond (Reed 63'), Elyounoussi (Davis 46'), Austin (Gabbiadini 63')