Leicester had already beaten third-placed Tottenham at White Hart Lane in January but this resounding result against Manchester City was their most significant in a remarkable season.
The Foxes have now picked up 28 points on their travels and, although they were denied a sixth clean sheet in their past seven matches, this was another win earned by their solid defence.
Aguero's glancing header from teenage substitute Bersant Celina's cross meant Manchester City retained their record of only failing to score once at home this season, but they had toiled in front of goal for much of the match.
Claudio Ranieri's side travel to fourth-placed Arsenal next weekend - win there too, and people might be asking 'who can catch Leicester?' rather than 'can the Foxes really win the title?'.
Manchester City's defence again at fault
While Leicester's defence was a solid and well-organised unit, given further protection by N'Golo Kante and Danny Drinkwater in central midfield, Manchester City looked nervy whenever the visitors came forward.
Martin Demichelis was left flat-footed by Robert Huth for Leicester's first goal and was beaten with ease by Mahrez for their second, while Huth was completely unmarked when he made it 3-0.
Things could easily have been even worse for home boss Manuel Pellegrini in his first game at the Etihad since it was announced Pep Guardiola would be replacing him in the summer.
Leicester's Jamie Vardy twice broke clear to latch on to balls over the top and was only prevented from inflicting further damage by smart blocks by Joe Hart.
Man of the match - Leicester's Robert Huth
'Nothing is finished' - Pellegrini
Manchester City boss Manuel Pellegrini said he had "no complaints" about the result but insists his side's hopes of winning the title are not over.
Pellegrini told BBC Sport: "Leicester played better than us. Conceding a goal from a set piece after two minutes was very important for the game.
"We had chances but it was a difficult game. I expected more from the beginning because it was very important, we are at home and playing top of the table, but we couldn't do it.
"There are 36 points to play for, nothing is finished. It is important for us to recover our players and I am continuing to not give up because we got an unexpected defeat but we must continue."
'We play without pressure' - Ranieri
Ranieri saluted his side's defensive discipline at the final whistle, telling BBC Sport: "We played very, very compact and believed everything could be possible.
"We play without pressure because we don't have to win the league. We must enjoy. This league is so strange and now it is important to think about Arsenal.
"I want to wait until the end of April because I know the last matches are very tough. This is a fantastic moment for the Premier League, nobody knows who can win it."
While Leicester head for the Emirates and another test of their title mettle, Manchester City must pick themselves up for the visit of another in-form team, Tottenham, before starting a run of fixtures that sees them play in the FA Cup, Champions League and the Capital One Cup final in the space of a week.
The stats you need to know
Robert Huth has scored more goals in his last five Premier League appearances (3) as he had in his previous 86 in the competition (2).
This was only the second time in his Premier League career that he's scored more than once in a game, with the German last scoring two in February 2011 for Stoke v Sunderland.
Riyad Mahrez (14 goals, 10 assists) became the first player to reach double figures in terms of both goals and assists in the Premier League this season.
Mahrez ended a personal Premier League goal drought of 11 hours and two minutes with his strike in this match.
Manchester City have not beaten any side currently in the top six of the league this season (W0 D3 L4).
Manchester City have lost as many league home games this season (3) as they had in 2014-15 and 2013-14 combined under Manuel Pellegrini (3).
Leicester City have lost just one of their last 16 league away games (W10 D5 L1).