Chris Wood headed his ninth goal in as many matches since joining the Foxes from West Brom at the start of the year before Harry Kane marked his home debut with a goal.
Leicester dominated the first half with goalkeeper Kasper Schmeichel a mere bystander, aside from a stunning save to keep out a Morton Gamst Pedersen volley with the game goalless.
A comparatively quiet second half ended with Andy King heading a third in stoppage time.
After five straight league wins at the turn of the year, it ended a three-game run without a victory and moved the Foxes within five points of second-placed Watford with a game in hand on Gianfranco Zola's team.
Leicester started brightly and Kane in particular looked sharp early on, the on-loan Tottenham teenager forcing a save, albeit a comfortable one, from Jake Kean after three minutes.
But soon afterwards he had the Blackburn goalkeeper scrambling across his six-yard line following a driving run and shot that trickled narrowly wide via the fingertips of Kean.
Danny Drinkwater's dipping 25-yarder then looped just over the bar, while at the other end, an outstanding save from Schmeichel prevented Blackburn from stealing the lead.
When a corner was only cleared as far as the crescent on the edge of the box, Pedersen struck a volley that took a deflection and looked like wrong-footing Schmeichel. But the Foxes keeper seemingly changed direction in mid-air to acrobatically tip the ball over the bar.
Kean, as he did with an earlier effort from Kane, then just did enough to keep out Ben Marshall's shot from the edge of the area.
From the resulting corner, on-loan Manchester United centre-half Michael Keane blazed over from inside the six-yard box when it seemed easier to score.
Leicester finally made the breakthrough in the 29th minute. Marshall beat his man down the right and whipped in a far-post cross that Wood nodded home.
Marshall was the provider again after 42 minutes when Kane got the goal he had threatened.
It was not unlike Wood's goal, with Kane heading in unmarked at the back post from a corner.
The 19,561 freezing cold fans inside the King Power Stadium were then starved of any notable action until the 77th minute.
Substitute Lloyd Dyer, on as a 75th-minute replacement for Anthony Knockaert, almost made an immediate impact as he skipped past his man down the left and got into the box but Kean was quickly out at his feet to block the shot.
A Wood curler went narrowly wide before King completed the scoring with a glancing near-post header from another Marshall corner.