The opening goal came within a minute of the restart amid considerable offside controversy.
Raheem Sterling is in sensational form.
Guardiola was frustrated by the questions about officiating and complicated rule system, just as he was irked by a report on the eve of the game that he had verbally agreed to join Juventus on a four-year deal.
Yet if the opener was debatable, there was no argument about the other two as Sterling made it 15 league goals for the season.
"We're just taking it a game at a time".
Following prolonged discussions between the match officials, the goal was awarded despite Sterling being in an offside position when Aguero touched the ball into his path, because Janmaat played it against the England winger's shin for the ricochet into the net.
'No, I didn't hear what (the referee) was saying but at the time I didn't think I was offside, so I was hoping he did have a long think and give us the goal and that's exactly what he's done, ' the England global told CityTV.
'I happened to get the luck, so I am happy with that.More news: Donald Trump calls Democrats 'an anti-Jewish' party
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They face Burnley on Sunday in a must-win game as they look to keep the pressure on the league leaders.
But after such a hard opening period, no-one would have expected that the game would have been settled decisively in City's favour in the opening quarter of an hour after the break.
"In the first half we had a very good performance - better defensively because we were well organised", manager Gracia said. "We did not take the second half seriously", Pochettino said.
Jurgen Klopp's side are now one point behind City in second place in the league.
Gracia threw on Deeney and Deulofeu in the 66th minute and it took 17 seconds for them to make an impact, Deeney heading down to the Spaniard who slotted home.
The UEFA and Premier League cases have been sparked by leaked City correspondence published by German media outlet Der Spiegel.
Elsewhere in the Premier League, Tottenham Hotspur suffered a shock 2-1 defeat to Southampton while Newcastle, Leicester, Bournemouth, Cardiff and Brighton all picked up wins.
Hopefully next season, like in Europe, they can accept that we install VAR in this situation and it will be fair.
To get the latest soccer news, text "SPORTS" to 22840. The three goals were fantastic but he can do better.