Burnley goalkeeper Tom Heaton also saved from Aguero, Aymeric Laporte and Bernardo Silva in a City performance that was average for long spells – but the main priority of three points was achieved and they know victory at home to Leicester City and away at Brighton will ensure they keep the crown.
City have been put to the test since their Champions League quarter-final exit against Tottenham – and they have responded in the manner of champions with three wins without conceding a goal.
Earlier, Jamie Vardy scored twice as Leicester dented listless Arsenal’s hopes of qualifying for the Champions League with a dominant victory at the King Power Stadium.
The unmarked Youri Tielemans headed in a cross from James Maddison just before the hour mark, then Vardy struck late on with a header and a tap-in from close range.
Arsenal played almost an hour of the contest with 10 men after Ainsley Maitland-Niles was sent off.
A third successive Premier League defeat left them two points behind fourth-placed Chelsea, who drew 1-1 with Manchester United at Old Trafford in yesterday’s late kick-off.
A mistake by goalkeeper David de Gea gifted Chelsea an equaliser as Manchester United’s hopes of playing in next season’s Champions League faded at Old Trafford.
With United leading through Juan Mata’s goal against his former club, De Gea spilled Antonio Rudiger’s 30-yard attempt for Marcos Alonso to level shortly before the interval.
It was a costly error by the Spaniard, whose form has come under scrutiny in recent weeks, although De Gea did come to his side’s rescue deep in stoppage time to deny Gonzalo Higuain a dramatic winner.
Up until Chelsea’s equaliser, United had been in control yet they remain sixth in the table, three points behind fourth-placed Chelsea with two games to play, after a third successive league game without a win.