With West Ham not in action due to Blackpool's participation in the FA Cup, Saints had the chance to move to the top of the league.
And they took it in fine style, with Jos Hooiveld, Aaron Martin, Adam Lallana and Tadanari Lee all on target.
Hooiveld put Nigel Adkins' men in front from a corner but they wasted several chances and had to wait until 12 minutes after half-time to double their lead.
Martin finished from close range after another corner, while Daniel Fox completed his hat-trick of assists by teeing up Lallana.
Lee then scored his first goal for Southampton as they extended their unbeaten run in the league to five games.
Mid-table Derby started the second half well but the hosts' second goal broke their spirits and they are now without a victory in six league and cup games.
Saints made two changes to their side, with Dan Harding and Richard Chaplow replacing the injured Frazer Richardson and Guly, who missed out due to illness.
John Brayford and James Bailey came back into Derby's line-up as Craig Bryson and Callum Ball made way.
Beaten by Reading in midweek, the visitors were coming up against a Southampton side who had only lost twice at home in 16 games this season.
And Saints showed plenty of attacking intent in the early stages, with Harding's free-kick from the right wing forcing Derby goalkeeper Frank Fielding to make a save.
However, there was nothing he could do as Hooiveld gave the hosts a 15th-minute lead. Fox's corner from the left was bundled in at the far post by the former Celtic defender.
Lallana was giving Derby's defenders a headache as the half wore on and the winger curled wide from a good position before he also missed the target after taking advantage of Shaun Barker's misplaced pass.
Against the run of play, Tom Carroll nearly levelled matters but his fierce low effort was magnificently kept out by Saints stopper Kelvin Davis.
Immediately after, Fielding was called upon to make equally impressive stops from Jack Cork's 20-yard strike and Rickie Lambert's long-range free-kick to keep the deficit to one goal at the interval.
The Rams showed greater urgency after the break but, after Lallana's header was brilliantly tipped over by Fielding, Southampton doubled their lead from the resulting corner.
Another Fox delivery, this time from the right byline, was fired high into the net by Martin at the back post in the 57th minute.
And the game was ended as a contest as Lallana finished off a great flowing move from the hosts eight minutes later. Cork fed Fox on the overlap and his cross was tucked away by Lallana.
Substitute Lee sealed a thumping triumph for Southampton with a spectacular blast into the top corner from the edge of the area 15 minutes from time.