Kevin De Bruyne pulled the strings throughout in another majestic display for the champions-elect, but Aguero stole the headlines with a four-goal haul which takes him level with Mohamed Salah in the Premier League's top-scorers list.
Leicester welcomed Riyad Mahrez back into their matchday squad for the first time since his desired deadline day switch to Man City broke down, although the wantaway winger had to make do with a place on the bench against the team he was desperate to join.
The spotlight soon switched to another winger as Man City broke the deadlock inside three minutes, with Sterling going some way to atoning for his costly miss against Burnley last weekend by this time converting from close range.
De Bruyne's beguiling ball into the box left the defence helpless before just eluding Aguero, but Sterling was there at the back post to tap it in for his 20th goal of the season, 15 of which have now come in the Premier League.
Leicester responded well to that early setback, though, and while the Foxes continued to surrender the lion's share of possession, they did manage to limit the home side's momentum and chances in the immediate aftermath of the opening goal.
City did have an opportunity to double their advantage when Aguero broke into the box at the end of a counter-attack, but Christian Fuchs stepped in to dispossess the striker and within seconds Leicester had the ball in the back of the net at the other end.
Nicolas Otamendi's loose pass was pounced upon by Vardy, who skipped away from Oleksandr Zinchenko and Ilkay Gundogan before getting the better of Aymeric Laporte and drilling his finish into the bottom corner via a slight deflection.
In doing so Vardy became the first player to score past Man City, Manchester United, Arsenal, Chelsea, Liverpool and Tottenham Hotspur in the same season, while also taking his league-leading tally to 23 goals in his 43 appearances against the league's 'big six' since his debut in August 2014.
It was the visitors' first and only meaningful attacking threat in the opening 45 minutes, but they were more than holding their own in general play and Schmeichel kept Bernardo Silva at bay from a tight angle shortly before the half-hour mark.
The Leicester keeper was also called upon to deny Fernandinho and De Bruyne within the following five minutes, but he was beaten all ends up in the 41st minute when Sterling latched on to a De Bruyne pass before taking it around Schmeichel, only for Aleksandar Dragovic to produce a goal-saving block on the line.
The two sides went into the break all square but, just as was the case in the first half, Man City made a quick start to the second and were back ahead within three minutes of the restart.
Once more the imperial De Bruyne was the creator, delivering another sumptuous pass into the box which left the defence and goalkeeper helpless as Aguero tapped it in at the back post.
The goal marked the first time Aguero had scored in seven consecutive home games for Man City, and within five minutes he had doubled his personal tally when he fired past Schmeichel after once again being found by De Bruyne, who also racked up three assists in a single match for the first time in his Man City career.
Leicester welcomed back Mahrez from his self-imposed exile in the second half, but that did little to change the course of the match as Otamendi came close to a fourth with a looping header which dropped just past the far post, before Bernardo almost got in on the act himself with a curling effort which had Schmeichel beaten but drifted narrowly off target.
Otamendi then drew another save from Schmeichel, but the Leicester keeper was at fault for City's fourth when he gave the ball straight to Aguero when trying to play out from the back, allowing the Argentine to lift his finish over the stranded shot-stopper and into the empty net for his hat-trick.
The goal saw Aguero move level with Thierry Henry as the foreign players with the most Premier League hat-tricks, on eight apiece, while he also became only the fourth player - alongside Alan Shearer, Henry and Harry Kane - to score at least 20 goals in four consecutive Premier League seasons.
The Argentine was not finished there, though, and he saved the best for last as he capped off the rout in the final minute of normal time, unleashing an unstoppable dipping strike from outside the area which crashed off the underside of the bar and in.
It was an emphatic way to cap off yet another convincing performance as Man City made it 19 consecutive home wins across all competitions, while also equalling a club record by scoring three or more goals in six successive home league outings.
Pep Guardiola's side will now turn their attention to cup duties for the remainder of the month, with Champions League, FA Cup and EFL Cup matches to come before they are next in Premier League action against Arsenal on March 1.
MAN CITY (4-3-3): Ederson; Walker, Otamendi (Stones, 81'), Laporte, Zinchenko (Danilo, 65'); De Bruyne, Fernandinho (Foden, 80'), Gundogan; Bernardo, Aguero, Sterling
LEICESTER (3-5-2): Schmeichel; Dragovic, Maguire, Fuchs; Albrighton, James, Ndidi, Silva (Simpson, 46'), Chilwell (Iheanacho, 62'); Diabate (Mahrez, 62'), Vardy