After going close several times, Aguero celebrated his return to the starting XI by wriggling through Chelsea's defence to score a 31st-minute opener before Kompany and Fernandinho made the game safe late on.
The well-earned victory continued Cityʼs impressive start to the season following their 3-0 win at West Bromwich Albion and gave manager Manuel Pellegrini a first win over his nemesis Jose Mourinho since the Portuguese returned to Chelsea in 2013.
“To win 3-0 in two games, one against the champions – we are just starting the season, but itʼs important to play in the way we did today,” Pellegrini told Sky Sports.
However, Mourinho protested that the scoreline reflected a “fake result”.
“We were the best team by far in the second half. What they did in the first, we did in the second,” he said.
“We dominated and when they feel they are in trouble, and they felt [that], they changed Aguero and [Raheem] Sterling, they try to recover control of the game.
“It is exactly when they scored the second goal. For me, completely fake.”
Earlier on Sunday, Arsene Wenger breathed a sigh of relief as Arsenal got their title challenge up and running with a hard-fought 2-1 win at Crystal Palace.
After slumping to a dismal 2-0 defeat against West Ham United in their opening game, Wengerʼs side had no margin for error at Selhurst Park if they wanted to avoid being cast adrift in the title race.
They rose to the challenge, securing a first league win of the season thanks to Olivier Giroudʼs superb 16th-minute volley and a Damien Delaney own goal in the 55th minute after Joel Ward had blasted Palace level.
It was a much-needed confidence boost for the Gunners and Wenger conceded it would have been hard to recover if they had left Selhurst Park empty-handed.
“Iʼm very pleased with the three points. If we had gone two games and zero points it would be absolutely difficult and we knew this would be a tricky one,” Wenger said.
On Monday (August 17), Christian Benteke scored a contentious first Liverpool goal as his team shaded promoted Bournemouth 1-0 at Anfield to claim their second victory of the Premier League season.
The teamsʼ first ever league meeting was settled Benteke”s 26th-minute strike in front of the Kop, but Bournemouth felt that in attempting to play the ball before it reached his team-mate, Philippe Coutinho had been offside.
“Thankfully the goal counted and weʼre happy to get the win,” said Rodgers.
“Iʼm pleased we've got two wins, six points and two clean sheets. The defensive organisation has been good. Thereʼs a lot of players coming into the club and itʼll take them a wee bit of time to bed in.”
Having previously won 1-0 at Stoke City in their opening game, Liverpool moved level on points with Manchester City, Leicester City and Manchester United at the top of the two-game table.
Meanwhile, on Saturday (August 15), Leicester City brought West Ham United crashing to earth with a 2-1 victory at Upton Park.
West Ham were 2-0 down by half-time as Japan striker Shinji Okazaki headed in his first goal in English football and Riyad Mahrez scored his third goal in two games.
Dimitri Payet replied for West Ham, but it was not enough to prevent Claudio Ranieri's from sealing their second win of the season.
Swansea City also built on an impressive opening performance, following up their battling 2-2 draw at champions Chelsea with a 2-0 win at home to Newcastle United.
Elsewhere, a late Stoke City fightback prevented Tottenham Hotspur claiming a first win of the season in a 2-2 draw at White Hart Lane.
Beaten 1-0 by Manchester United on the opening day, Spurs, who welcomed back goalkeeper and captain Hugo Lloris, went 2-0 up through an Eric Dier header and a deflected Nacer Chadli volley.
But after Spursʼ striker Harry Kane had been taken off, Stoke stormed back to level courtesy of a Marko Arnautovic penalty and a Mame Biram Diouf header.
Earlier, Romelu Lukaku scored two first-half goals and Ross Barkley added another as Everton claimed their first victory of the season by winning 3-0 at Southampton.
Belgium striker Lukaku headed home Arouna Koneʼs 22nd-minute cross and swept in from Barkleyʼs astute pass on the stroke of half-time before the England midfielder neatly curled in a third goal six minutes from time.
Sunderland's early-season woes continued as they went down 3-1 at home to promoted Norwich City.
Goals from Russell Martin, Steven Whittaker and Nathan Redmond put Alex Neil's visitors in command at a sombre Stadium of Light, before 21-year-old substitute Duncan Watmore replied for Sunderland.
“Together, we have to find out if we can find the solution,” said Advocaat.
Watford, another promoted side, remain unbeaten but also winless after a goalless draw at home to West Bromwich Albion.
Whilst on Friday night (August 14), Adnan Januzaj marked his Manchester United return with a goal as Louis van Gaalʼs side beat Aston Villa 1-0 to claim a second consecutive Premier League victory.
Making his first start since February, Januzaj converted a glorious pass from Juan Mata on the half-hour as United extended an unbeaten record in league games at Villa Park that now stands at 20 years.
“I think we have played better than last week, certainly in the first 25 minutes,” said United manager Van Gaal. “But after we scored the goal, we were running out of the game. We had a lot of unnecessary ball losses.
“I'm very pleased, because you can't get more points than six,” he added.