Guardiola's men failed to scale the dazzling heights of recent performances, with a tenacious and disciplined Burnley display causing them moments of discomfort before quickfire goals from Nicolas Otamendi and Leroy Sane made victory safe inside the final 20 minutes.
Aguero opened the scoring with a 30th-minute penalty after Bernardo Silva went down under a challenge from Nick Pope, the Burnley goalkeeper who then produced a pair of brilliant saves to prevent the Argentina striker from surpassing Eric Brook's all-time City record of 177 goals.
Guardiola's free-scoring side struggled for clear openings early on and might have gone behind in the 15th minute when Chris Wood capitalised on slack defending by Kyle Walker, but City goalkeeper Ederson was alert to the danger.
Wood's impressive start to the game was cut short by an injury sustained in that challenge and Ashley Barnes replaced the New Zealand international.
David Silva finally got City round the back of their opponents in the 23rd minute but Bernardo Silva shot too close to Pope from Sane's cutback.
An even more impressive David Silva pass put Kevin De Bruyne one-on-one with Pope five minutes later and the goalkeeper saved before making an ill-judged dart from his line to deny Bernardo Silva on the rebound.
Whether there was enough contact to send the Portugal international sprawling in such a fashion was debatable but it convinced referee Roger East and, after a brief melee involving players from both sides, Aguero did the rest.
One to go!pic.twitter.com/qEyinO9SYn— Manchester City (@ManCity) October 21, 2017
Some ponderous possession near their own goal from City almost coughed up a Burnley equaliser, with Scott Arfield's resulting shot deflected behind, while Pope twice denied Aguero brilliantly with his feet as City's striker sensed history on the stroke of half-time.
Burnley had a penalty shout turned down six minutes into the second half when Fabian Delph hit a clearance against his own arm. Jack Cork was booked for his protests before City defended subsequent set-pieces unconvincingly.
David Silva skewed a drive wide when Sane and Aguero appeared better placed and a pair of menacing De Bruyne crosses as City reasserted themselves after the hour were the sum of Burnley's concerns until they were punished once more by an Argentina international.
With Aguero's threat subsiding before his eventual substitution, centre-back Otamendi rose to power in Sane's left-wing corner in the 73rd minute, with Steven Defour's efforts on the goalline leaving something to be desired.
De Bruyne had experienced a relatively quiet outing but added to his majestic catalogue of assists with a wonderful sweeping pass into Sane's path and the Germany winger chalked up his seventh of the season with an unerring finish.
Aguero's replacement Gabriel Jesus similarly found Pope in his way as he looked to add gloss to the scoreline – a margin of victory that would have been unjust on Sean Dyche's side as their undefeated away run came to an end.
Key Opta stats:
- This is Manchester City's joint-best points return after the first nine games of a Premier League season alongside 2011-12. The only team with more points at this stage of the season were Chelsea (27) in 2005-06.
- Pep Guardiola has won 25 points so far this season with Man City; only in 2015-16 (27 pts with Bayern Munich) has he won more points as a manager from the opening nine games of the season.
- Leroy Sane has both scored and assisted in three of his last four Premier League appearances for Man City.
- Since his Man City debut in September 2015, Kevin De Bruyne has provided 33 assists in the Premier League, more than any other player.
- Burnley failed to land a single shot on target in this match.