Sergio Aguero, who had ineffectively ambled through the first half, scored twice in 94 seconds; Leroy Sane added a sumptuous third and set up the fourth for Bernardo Silva, and with that Burnley's resilience was cracked.
Burnley led 1-0 but had conceded a free kick, 40 yards from their goal.
"Both of Sergio Aguero's goals were awesome, there were clever and quick and I am happy with both of his goals", Guardiola told reporters.
Bearing in mind City have a League Cup semi-final to play in midweek it would have been normal to see more rotation, but Guardiola opted to play one of his strongest teams in this game.
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The game also saw David Silva return from Spain where he was tending to his prematurely-born son.
"I'm happy he made the statement", said Guardiola.
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With Burnley's mean streak, the worst scenario was potentially for City to pull one goal back and force a replay at Turf Moor that neither side wanted.
Even if you don't support them, you have to sit back and appreciate Aguero and Gundogan's contributions.
"We had a game plan and I think it worked in the first half, but I think a 10 minute spell from their first killed us a little bit", Barnes added. Guardiola showed his killer instincts by sending for Kyle Walker and Kevin De Bruyne from the bench and City ensured there was no chance of a replay.
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". This is not to say they are just lumping the ball into the box and hoping for a header, but rather that the forwards are making clever runs and the midfielders have the passing accuracy to find them. But after, of course, to give real value to what we have done so far, what we are going to do in the future, you have to lift the titles.
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