The Foxes dominated their East Midlands rivals throughout and the only surprise was the narrow margin of the win courtesy of a 50th minute strike by their top scorer David Connolly.
A win for Derby would have secured a play-off place and also seen them register a record 13 away victories in a season.
But defeat means they now face tricky games at Coventry and at home to Preston to gain the three points that would guarantee a top-six finish.
It was one-way traffic in the first half with Connolly blasting wide from 12 yards and Dion Dublin testing Lee Camp with a well-placed header inside ten minutes.
Patrick McCarthy joined the attack to almost connect with a Jordan Stewart free-kick and then Danny Tiatto rippled the side-netting from 25 yards.
Derby had to wait until the 23rd minute to muster their first attempt on goal when Marco Reich cut in from the right to flash a 15-yard shot wide.
The Foxes continued to give Derby the runaround and Dublin went close with a spectacular overhead kick which narrowly cleared the crossbar.
The second half began where the first had left off with Leicester surging forward and they finally broke through on 50 minutes with Connolly bagging his 12th of the season.
The Derby defence appeared to freeze as Tiatto hoisted a high ball from the left into the penalty area allowing the alert Connolly to race in and fire home through the keeper's legs from six yards.
A goal behind, Derby were now compelled to attack in numbers but Leicester's blue barrier, superbly marshalled by McCarthy, stood firm.
Ten minutes from the end, however, the Rams squandered their best chance of the match when substitute Ian Taylor blazed Tommy Smith's cross over the bar from 12 yards.
There was another scare in the final minute when another substitute, Paul Peschisolido, slipped the ball to Smith whose goalbound shot was superbly blocked by Ian Walker.