Second-half goals from Islam Slimani and Jamie Vardy made it five wins from five in the Premier League - and six from six overall - since Claudio Ranieri's departure from the club as the once relegation-threatened champions climbed into the top half of the table.
Sunderland, meanwhile, have now gone six consecutive matches without even scoring a goal and remain rooted to the bottom of the table, eight points from safety.
Under-fire visiting manager David Moyes was able to name Jermain Defoe in his starting XI despite concerns over a knock, while the visitors were also boosted by the return of captain Lee Cattermole, making his first league start since September.
Cattermole's presence seemed to make a difference as Sunderland more than held their own for long spells, but Leicester moved up a gear in the final 20 minutes to wrap up a sixth consecutive home victory.
The hosts created the first chance inside the opening minutes when Demarai Gray raced down the left flank and cut a low ball into the area for Shinji Okazaki, but the striker could not get enough on his finish to test Jordan Pickford.
Pickford was called into action after 16 minutes when Robert Huth latched on to a Riyad Mahrez free kick at the back post and sent a looping header towards goal which the Sunderland keeper safely tipped over his own crossbar.
Sunderland were arguably the better side in an uneventful first half, but their troubles in the final third continued and long-range strikes from Defoe and Didier Ndong which flew off target were their only efforts of note before the interval.
The Black Cats almost saw all of their hard work undone at the end of the first half when Gray cut inside from the left flank and curled a fine effort towards the far corner, only for Pickford to pull off a sensational fingertip save.
Gray was once again allowed to cut inside onto his right foot moments later as Leicester hit Sunderland on the counter-attack, but this time the youngster's curling strike dropped a few yards wide of the target.
The half-time whistle signalled nine hours of Premier League football without a goal for Sunderland, and they didn't show many signs of ending that run in the second half as Kasper Schmeichel was only forced into routine saves to deny Sebastian Larsson and Defoe.
Huth scored an own goal in the reverse fixture to send Sunderland on their way to one of their five wins of the campaign, but he almost redeemed himself shortly after the hour mark when he forced a smart low save from Pickford after latching on to a long Christian Fuchs throw.
Shakespeare turned to Marc Albrighton and Slimani off the bench in an effort to spark his team into life, and it proved to be an inspired decision as the pair combined for the opening goal just seven minutes after their introduction.
Albrighton was allowed to cut back onto his right foot before swinging a trademark cross into the middle for Slimani to glance past a helpless Pickford as Leicester finally found the breakthrough.
Sunderland's woes were best encapsulated during a 70-second spell shortly afterwards when Victor Anichebe saw a deflected effort hit the post before the Foxes killed the game - and possibly Sunderland's survival hopes - by doubling their lead at the other end moments later.
Again Albrighton was the creator as he burst down the left flank before cutting a low ball into the box for Vardy, who did not hesitate to lash his finish into the roof of the net.
Suddenly Leicester looked back to their old selves and they pushed for a third goal in the closing stages, with Pickford forced into saves to deny Andy King and Mahrez before Albrighton steered a shot of his own wide of the target.
Sunderland, on the other hand, looked resigned to their fate and never showed any signs of launching a late comeback as they slumped to a sixth consecutive top-flight match without scoring for the first time since 1981.
A little more than a month ago the Black Cats were just two places and two points behind Leicester, but the Foxes now sit in 10th place and boast a 16-point advantage over Moyes's side, who look doomed for relegation to the Championship with only eight games of the season remaining.
Both went on to stop at six wins - a mark the Foxes have the chance to equal when they take on Everton at Goodison Park this weekend - whereas Sunderland host Manchester United at the Stadium of Light.