The Germany ace came up with two razor-sharp assists in two minutes - with Aguero delivering the goal on both occasions - to turn a 1-0 deficit into a 2-1 lead just before the hour mark at the Etihad Stadium.
The first was a quickly taken free-kick that surprised almost everyone but City’s record goalscorer.
Aguero sprung forward to smash home a first-time shot in the turn, before Gundogan laid on a delightful back-heel for Aguero’s second.
Of the first goal Gundogan declared: “It was a free-kick and the referee didn’t tell me to wait, so I had some eye contact with Sergio because I know he likes to use these kind of situations to play quick.
“As soon as we had the contact I was sure he was going to make the run, so I just had to play the pass and fortunately, it was allowed, and I think that was correct, we just reacted quicker.”
City 4-1 Burnley: Guardiola reaction
The crowd had barely taken their seats before the Gundogan-Aguero combination struck again.
“The timing was just perfect.” Gundogan said of his backheel. “Sergio passed the ball to me, I was waiting for a run and Sergio was just at the right time in the right spot, so I was quite sure this ball was going through.
“Luckily both actions were a goal and 2-1 was very important at that point - especially after the first goal gave us a boost and after the 2-1, all our confidence was back and we kept the ball and started to play very well, scored two more goals and we are very happy with the result.”
Reflecting on the match as a whole Gundogan said: “In the second half we just wanted to score you know. In the box, in front of the box, I don’t think there was that much difference between the halves, because in the way we played, we were satisfied with the first half.
“Of course we conceded a goal that was maybe not necessary... but we accepted it and at half time the manager told us he was not unhappy with the first half - we just needed to continue and be more clinical in front of the goal - and he was right!”
Goals from Leroy Sane and Bernardo Silva rounded off the win and City go into the hat for Monday’s draw.
