As expected, the Blues had a tough game against a good team but dominated the match and scored the goals when it mattered to reach 11 straight wins in all competitions.
Manchester City playmaker Bernardo Silva defended himself against criticism from Burnley manager Sean Dyche amid controversy over the penalty he won in the Premier League leaders' 3-0 win at the Etihad Stadium.
He will surpass Brook and become the club's all-time record goalscorer with just one more strike for the Citizens.
Such form has led to Jesus being named in the three-player shortlist for the prestigious Golden Boy award alongside Kylian Mbappe and Ousmane Dembele - quite an achievement after arriving in Europe only in January.
Silva went down under a challenge from Burnley goalkeeper Nick Pope to win the penalty and Dyche was unimpressed with what he judged to be a theatrical tumble from the Portugal international. "It hurt a little bit and for me it was a penalty".
Manchester City travel to the Hawthorns to face West Bromwich Albion in their next league game.
Up until that point, Burnley had shown that discipline that has made them so hard to beat on their travels this season; City laboured for clear openings early on, and might even have gone behind after a quarter-of-an-hour.
Aguero remained calm throughout the confusion and, having missed from the spot on his last appearance, made no mistake to put City ahead and equal the record.
Brook's goals came in 450 appearances prior to the Second World War.
His tally includes 10 hat-tricks and his most famous City goal was his 30th - the dramatic last-gasp strike to clinch the Premier League title in 2012.
"Another clean sheet is so important [too]".