City began in now familiar fashion, pressing high with plenty of possession and it was no surprise when Sergio Aguero put the Blues ahead with just eight minutes on the clock.
Bacary Sagna played the ball to Aguero in the box and the Argentine's sublime first touch gave the space to drill a low shot through the legs of Fabianski for his tenth goal of the campaign,
But Swansea had already made a couple of probing attacks in the final third and looked up for the battle ahead and within five minutes, the hosts were level. made a superb save from Llorente on 12 minutes, but failure to clear the danger saw the ball dinked into the box again and as Sagna lost his footing allowing Llorente to power a half-volley in the top right-hand corner from 15 yards.
Both sides had chances before the break but City came closest to re-taking the lead when Kevin De Bruyne's free-kick was headed back across goal by Nicolas Otamendi and Aleksandar Kolarov had the ball whipped off his toes just as he was about to score ensuring the teams went in level at half-time.
Swansea had clearly done their homework and learned from their midweek loss to City as they continued to threaten after the re-start and Wayne Routledge had a clear chance to give the home side the lead within five minutes but he dragged a low angled shot wide with only Bravo to beat.
The Blues looked set to go ahead just before the hour-mark as David Silva's low cross found Aguero only for Amat to make a last-ditch tackle to save his team. Then Raheem Sterling mis-hit a shot from close range after good work by Aguero and De Bruyne as City upped the ante somewhat.
Then, halfway through the second period, the break City needed.
De Bruyne collected the ball just inside the box and Mike van der Hoorn's flailing arm caught the Belgian in the face and the referee pointed to the spot. Aguero stepped up to calmly chip the ball high into the back of the net with Fabianski going the wrong way.
Silva's deflected shot almost made it 3-1 on 74 minutes but Fabianski just managed to tip the ball over and from the resulting corner Fernandinho should have scored with a header that flashed wide.
At last, the goal City's dominance deserved arrived on 77 minutes with a counter-attack that had four against two home defenders at ome stage and just when it seemed Sterling had held on to the ball too long, the England winger produced a clever step-over that bamboozled Kyle Naughton before slipping the ball home to the delight of the travelling Blues.
There were chances to add more to the tally, but nobody was complaining after another excellent three points - and this with City not at their devastating best.
The penalty award with the game still finely balanced finally gave City a much-needed breakthrough. Up to that point it still could have gone either way but once Aguero slotted home the spot-kick, the Blues could have scored four or five goals with Swansea's heads visibly dropping,
Man of the Match
Two more goals and 11 for the season for the prolific Aguero who is enjoying his most prolific start to a season yet with City. A constant threat, he was the main difference between the teams on the day.
Photo of the Match
What it means
City increase their lead at the top of the Premier League to four points following Everton's loss at Bournemouth. It also makes it 10 wins from 10 games as the Blues maintain their 100% record in all competitions.
A late injury to De Bruyne will be a concern ahead of the midweek trip to Celtic, though hopefully he won't be absent for too long if he has indeed picked up a knock.
How they lined up
Stats and Milestones
Aguero's double means he has now scored 28 goal in 27 Premier League matches
Kevin De Bruyne made his 50th appearance for City in all competitions
This was the sixth successive Premier League between City and Swansea game where both teams have scored
City are the first side since Chelsea in 2009 to win the opening six Premier League matches.
The Blues are just one game short of equalling the 11 successive wins Club record set by Manuel Pellegrini's team.
This was Aguero's 100th Premier League win with City.