Man City - who also had Fabian Delph sent off during the closing minutes - have now lost three of their last four league games and sit behind Tottenham Hotspur in the standings, while seventh-placed Leicester have recorded back-to-back triumphs over Chelsea and last season's top-flight champions.
The opening stages of the game were uneventful as Man City remained patient on the ball, but their discipline was rewarded before the end of the first quarter-of-an-hour as Bernardo put his team into the lead.
However, Leicester needed just five minutes to get back on level terms. Jamie Vardy was sent down the left and sent an inswinging cross towards the back post, where Albrighton directed a header into the far corner.
Man City responded with Kevin De Bruyne seeing a 35-yard strike comfortably saved by Schmeichel, but it took until the closing stages of the opening period for the visitors to create their next clear-cut chance.
Leroy Sane got in down the left before pulling the ball back for Aguero, but the Argentine could only hook a shot over the crossbar from eight yards.
Leicester rallied towards the end of the first half and Vardy could have put the Foxes in front after a mistake from Bernardo, but Ederson came out well to make a timely block after the forward had advanced into the penalty area.
The visitors had the better of the action after the restart, but the first shot of the second half came from James Maddison, who sent his effort wide of the far post from 25 yards out.
City continued to dominate possession, but Guardiola's side were struggling to create any opportunities with only Aguero looking a threat in and around the penalty area.
Delph saw a 20-yard strike easily saved by Schmeichel and Aguero headed harmlessly wide, and the game reached a stage where Leicester would have settled for a point.
However, the Foxes completed the turnaround with nine minutes remaining. A poor corner was only half-cleared into the path of Pereira, who found the far corner with a thunderous effort from 20 yards.
Sane blazed a late effort over from the edge of the area before Delph was given a straight red card for a lunge on Pereira, but Man City did not look like forcing an equaliser and are now considered outsiders to retain their Premier League crown with Liverpool having eased past Newcastle United.
LEICESTER CITY (4-3-3): Schmeichel; Pereira, Morgan, Maguire, Chilwell; Choudhury (Gray 63'), Mendy, Ndidi; Albrighton, Maddison (Simpson 78'), Vardy (Okazaki 88')
MANCHESTER CITY (4-2-3-1): Ederson; Danilo, Stones, Laporte, Delph; Gundogan, De Bruyne (David Silva 70'; Sane, Bernardo (Mahrez 83'), Sterling; Aguero