After a goalless first period, Daka opened the scoring on the hour mark with a simple finish from close range before then converting from the penalty spot five minutes later after he was fouled by Rotherham goalkeeper Viktor Johansson.
Foxes substitute Cesare Casadei completed the scoring with a diving header in the 72nd minute as the home side secured a fifth straight league win to extend their lead at the top following Ipswich's heavy defeat at Leeds in the early kick-off.
Rotherham remain rooted to the foot of the table, nine points from safety, having lost all matches under new boss Leam Richardson and are winless in their last 11 league games.
The Foxes created the game's first chance when a short corner was played to Kiernan Dewsbury-Hall who cut in from the left before curling a shot well over the crossbar.
Soon after, Dewsbury-Hall burst into the box only to be denied by Johansson who was quick off his line to smother the midfielder's effort.
Nigeria international Wilfred Ndidi was next to try his luck, driving a low shot straight at Johansson from distance.
Clear-cut chances were at a premium in the first half, as Stephy Mavididi blazed a volley high into the stand when left unmarked at the back post.
And shortly before half-time, Foxes defender Wout Faes blasted an effort over the bar in frustration from 25 yards.
Leicester almost broke the deadlock early in the second half when Abdul Fatawu caught Hakeem Odoffin in possession inside his own box only for Sean Morrison to make a superb goalline clearance and deny Daka the opening goal.
Johansson then made a crucial save to keep out Ricardo Pereira's shot from inside the box before bravely claiming the loose ball.
However, the Foxes finally made the breakthrough on the hour mark as Daka finished from close range after Johansson saved Faes' initial effort and Ndidi miskicked the ball into the scorer's path.
And the home side won a penalty four minutes later when Daka took the ball around Johansson only to have his legs taken away by the goalkeeper after the Millers were caught in possession deep inside their own half.
Daka duly picked himself up to coolly fire the resulting penalty into the bottom left corner and score his fourth goal in as many league matches.
Leicester made sure of the points 18 minutes from time when substitute Casadei placed a diving header into the bottom right corner from Pereira's cross from the left, just two minutes after coming off the bench.
The Foxes have now scored three or more goals in each of their last four games while Rotherham are winless on the road in 24 matches dating back to November 2022.