City absolutely dominated the game at Eithad Stadium, but former Barcelona player Victor Valdes produced an inspired performance in the Boro goal to ultimately deny Pep Guardiola, with whom he enjoyed four glittering years in Catalonia.
Aguero had pounced late in the first half to put City ahead following a frustrating opening period.
However, the Teessiders left Arsenal with a point in their last away game, had only lost once on their travels previously, and the menace they had showed on the break elsewhere this season slowly came back into their game.
It was an unlikely goalscorer, De Roon, who popped up to thump a header past the helpless Claudio Bravo in stoppage time, sending Boro fans into raptures.
Evoking memories of their 2-0 FA Cup win here as a Championship club two seasons ago, Boro’s impressive defence looks to be the making of their Premier League survival bid.
Guardiola, however, will lead the inquest into how his side managed not to win this game and failed to back up their stunning 3-1 Champions League success over Barcelona in midweek, with Arsenal and Liverpool now able to knock them off top spot.
Boro clung on for grim life in a first half that saw City resume their typical gameplan of stifling possession after Tuesday’s counter-attacking brilliance.
However, for all that Guardiola’s team probed and passed, Middlesbrough – and especially Valdes – met them with stern resistance.
Aleksandar Kolarov, Aguero and David Silva were all repelled by Guardiola’s former Barca number one, with Valdes and the centre-back pairing of Calum Chambers and Ben Gibson also on hand to cut out a string of low crosses from either flank, a tactic City persisted with until it finally worked two minutes from the interval.
Kevin De Bruyne drifted to the right flank before managing to squeeze his cross between defence and goalkeeper, with Aguero ghosting in to prod home a landmark goal from close-range.
Jesus Navas thumped the post with the last kick of the first half and City were put on warning immediately after the restart when the otherwise isolated Alvaro Negredo almost caught Claudio Bravo off his line from fully 50 yards and the Chilean was forced to smother Adam Forshaw after the visitors sliced through Guardiola’s defence.
Stewart Downing’s cross-shot was wasteful after De Roon had sprung the visitors into a rare breakaway and Aguero and De Bruyne both blazed over when they ought to have put the game to bed.
And they were made to pay in stunning fashion as De Roon met George Friend’s cross and thunder his first Premier League goal home.