McGoldrick has now scored four goals this season (Getty)
Southampton striker David McGoldrick grabbed the only goal as a lacklustre Derby were booed off at Pride Park.
Rams keeper Roy Carroll made a number of fine saves to keep the scores level.
But Saints deservedly took the lead just before the hour when McGoldrick netted from close range after Adam Lallana had fired against the bar.
MCGoldrick later smashed a shot against the bar while the home side rarely threatened and have now not won a league match since September last year.
Derby assistant boss Chris Hutchings: "We have got good players at this club but they've let themselves down, they've let their team-mates down and they let the fans down.
"We were second to everything, we were a yard slower and our passing was off.
"If it hadn't been for our goalkeeper Roy Carroll we could have been beaten by three, four or five. It was very poor."
Southampton head coach Jan Poortvliet: "I am very happy with our first win and I thought that we deserved it.
"I thought the team were outstanding today and that is a big compliment to pay because we had a lot of young boys out there.
"I hope that we can get into the play-offs this season."
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