The Vanarama Conference strugglers looked to have earned a replay but in the third minute of added time, skipper Luke Foster brought down Johnny Russell and Chris Martin made no mistake from the spot.
That was cruel on Southport and their goalkeeper David Raya Martin, who had made a string of magnificent saves to frustrate Derby and head coach Steve McClaren - who made nine changes.
Even so, there were still five full internationals in the Derby line-up which highlighted the size of the task facing the team 89 places below them in the football pyramid.
However, the 2,700 visiting fans were given early encouragement when a weak header by Lee Naylor let in Mitchell Austin in the fifth minute, forcing Derby keeper Kelle Roos to dive at his feet to push the ball away.
Southport threatened again in the 11th minute when Paul Rutherford got behind Derby on the left only for his cross to be blocked - but Derby should have scored in the 20th minute when Leon Best blazed wildly over from eight yards out after Craig Bryson's low cross-shot had come back off Raya Martin's post
Bryson was becoming increasingly influential and it needed an excellent tackle from Scott Kay to deny the Scottish midfielder when he darted through onto Omar Mascarell's pass in the 28th minute
Another precise pass by the on-loan Real Madrid player put Best clear on the half-hour but he had strayed offside and Bryson was through on the right two minutes later, only to slip as he shaped to cross.
The pressure was building and Raya Martin had to dive to his left to keep out a 25-yard drive from Paul Coutts in the 35th minute, before Simon Dawkins shot over from the edge of the area five minutes later.
Derby wasted another great chance in the 42nd minute when Dawkins and Naylor combined down the left - but Ryan Shotton put his header wide from six yards.
Southport had been on the back foot for long periods but they were still in the tie at half-time and Derby were given a warning in the 58th minute when a deflected cross gave Richard Brodie a chance - but he could not get enough power on his header.
The visitors went close again two minutes later when Kay had a shot blocked and it was a sign of Derby's increasing anxiety when McClaren made three changes in the 63rd minute.
The Rams still could not break Southport down and the outstanding Raya Martin made another superb save in the 78th minute when he flew to his right to parry a Jake Buxton header.
However, Southport's resistance was finally broken when Russell was caught by Foster and although Raya Martin went the right way, Martin's penalty was too powerful and Derby breathed a huge sigh of relief.
Source : PA