The hosts have closed the gap to only three points between themselves and league leaders Arsenal, but Mikel Arteta's team can regain their lead when they play West Ham on Sunday.
The first 13 minutes saw two goals for Pep Guardiola's team, one from John Stones' thunderous attempt and the other from Haaland's penalty.
Twelve minutes later, the 22-year-old Norwegian goal machine added his second with a wonderful dinked finish, but he was replaced at halftime and was unable to add to his total.
The closest the hosts came to scoring a fourth goal in the second half was when goalkeeper Daniel Iversen made an outstanding leaping save to repel Riyad Mahrez's looping shot.
While Kelechi Iheanacho scored a consolation goal in the 75th minute and also struck the post against his former team, Dean Smith had a terrible start to his first game as Leicester's coach.
The Foxes, who are currently in 19th place and two points from safety, are still in serious difficulty at the wrong end of the table.
Arsenal clash looms large
As Manchester City's juggernaut continued to roll in their pursuit of a Triple Crown of titles, this match played out as expected.
Arsenal is under threat from Guardiola's team, and the Londoners cannot afford any mistakes given that City is in fine form right now thanks to a 10-game winning streak.
They defeated Bayern Munich in the first leg of the quarterfinals on Tuesday, and they now appear to be on track to go to the last four of the Champions League. On Saturday, they will play Sheffield United in the FA Cup semifinals.
But the crucial match against Arsenal, which might decide the title, is scheduled for April 26 at Etihad Stadium. The visitors are hoping to end their lengthy championship trophy drought and prevent their rivals from winning three straight championships.
Haaland, who is unstoppable up front for City and has scored 47 goals in 40 appearances across all competitions, is the team's main offensive threat.
With eight games remaining in the 38-game season, his spot-kick and cunning finish from Kevin de Bruyne's assist brought his total in the top division to 32, matching Mohamed Salah's record.
After Stones' spectacular first-time effort from the edge of the box had launched his team on their way, the former Borussia Dortmund striker's goals gave his team a 3-0 lead.
Both players were taken off at halftime with the victory all but assured, but Leicester stayed strong and the club was unable to score any more goals.
Foxes slump to another loss
After taking over for Leicester till the end of the season, former Aston Villa manager Smith did not have the best of starts as it was attack against defense.
The Foxes have one point in their previous nine games, showing little sign of improvement in a terrible season. Since Christmas, they have only accumulated eight points, the fewest of any top-flight team.
Ederson, the home goalkeeper, was essentially a spectator for the whole game, but after substitute Iheanacho had stabbed in from close range, he made a quick stop to deny James Maddison.
They were soundly defeated in the end, but the Nigerian striker also hit the post in the 90th minute, which might have set up a tense conclusion.
Jamie Vardy, a striker, made his 300th Premier League game, but the 36-year-old was unable to add to his eight goals against Manchester City before being replaced at halftime due to lack of supply.
After missing six weeks due to an ankle injury, Youri Tielemans made his comeback, and Caglar Soyuncu, a defender who had lost favor under Brendan Rodgers, made just his third league appearance of the year.
Despite reversing a disastrous start, Leicester lost for the 20th time in a row in the league, matching bottom-of-the-table Southampton in that regard.