The Foxes, who reached the last eight of the FA Cup with victory at Norwich last weekend, were well worth the three points and only Derby goalkeeper Frankie Fielding stopped the visitors from running riot at Pride Park.
He was beaten by Danns' first-half side-footed volley but the influential midfielder was thwarted twice thereafter by Fielding.
The former Blackburn keeper also produced an excellent save from David Nugent's header after the interval to set up a tense finale.
Try as Derby might however, they lacked a cutting edge up front and only Nathan Tyson looked threatening as they drew a blank for the fourth successive match.
Lloyd Dyer nearly doubled his side's lead as he struck the woodwork twice in a matter of seconds in the closing stages but the Foxes comfortably held on to complete the double over their opponents.
The visitors looked like they would be in for a tough game as Tyson's strike from just outside the area forced Leicester goalkeeper Kasper Schmeichel to make a save after just 15 seconds.
It was all Leicester for the remainder of the half, however.
Jason Shackell's block denied Jermaine Beckford after the striker had twisted and turned his way into the area.
Fielding then did well to parry away an effort from Danns and soon after the Leicester midfielder was hacked down by Jamie Ward, who may have been fortunate to escape with just a yellow card following a studs-up, over the ball challenge.
Danns would have his revenge as he broke the deadlock and gave the Foxes a deserved 16th-minute lead.
Dyer outstripped full-back Paul Green on the left and his cross to the back post produced a controlled volley from Danns that went across Fielding, who could only paw the ball into the net.
Danns continued to make a menace of himself and after being given plenty of room by Derby's defenders, he unleashed a 25-yard strike that was superbly tipped onto the post by Fielding.
The 29-year-old was once again given too much space and his left-footed strike from a similar distance forced Fielding to make the save.
Leicester could not make their dominanace count with a goal and they were nearly made to pay in the early stages of the second half.
The ball ricocheted to Green in acres of space in the box but by the time he had it under control, Leicester's defenders were able to charge him down and block the shot.
Tyson's left-footed strike from the edge of the area only narrowly missed Schmeichel's left-hand post as the hosts continued to search for a goal.
They were nearly caught out, however, as David Nugent's header at the front post from Ben Marshall's corner was magnificently palmed onto the crossbar by Fielding.
Dyer might have ensured victory in the the final minute but after hitting a post from a narrow angle, his rebound effort came back off the upright.