Fabregas found the top corner to become the first goalscorer against Sven-Goran Eriksson's City, who had won their first three games.It was particularly harsh on the imposing centre-back duo of Richard Dunne and Micah Richards, Richards' only mistake resulting in a penalty that Schmeichel saved from Robin van Persie.
And at the other end, Eriksson and his bench were up on their feet in the second half claiming a penalty when Kolo Toure flattened Michael Johnson, but Chris Foy waved play on, allowing Arsenal to take advantage.
• Sven upbeat after first loss
There would be no reunion between Eriksson and Theo Walcott, who the Swede took to the World Cup last year without playing, with the teenager not in the Arsenal squad.
There were still plenty of options for Arsene Wenger, with Emmanuel Adebayor back from a groin problem and Tomas Rosicky also returning as Arsenal looked to break down a stubborn City defence.
At the back, though, Philippe Senderos was injured in the warm-up and Gilberto came in at centre-half for his first appearance of the season, and within 19 minutes Mathieu Flamini was playing at right-back following an injury to Bacary Sagna.
The game developed into matter of Arsenal enjoying possession, with City looking to counter-attack and exploit Arsenal's makeshift defence.
Most of the time they were faced with the solid partnership of Richards and Dunne, so Van Persie tried his luck from long range and cleared the crossbar.
City chances in the first half were more convincing. Johnson burst through the Arsenal defence to set up Martin Petrov for an effort that went wide.
Emile Mpenza, in for the injured Valeri Bojinov, had an even better chances after Petrov sent him through, but the striker made poor contact on his effort.
Elano had the best of the first-half chances for City, but he barely tested Manuel Almunia with a shot from the area when he had team-mates waiting for a pass.
At the other end, goalkeeper Schmeichel required treatment after claiming the ball when Van Persie ran through. The Holland forward appeared to leave a boot in, but he also apologised as the goalkeeper was treated.
Richards has earned praise for his impressive start to the season, and his form continued as he threw everything to block Arsenal's attacks. Dunne did the same as the hosts looked to convert their possession into chances.
They got closer in the 36th minute after Stephen Ireland's poor pass gave them the ball, but Van Persie was inches away from Fabregas' cross.
Van Persie crossed from a similar angle three minutes from the break but had no team-mates in the six-yard box.
Adebayor had an early effort from the edge of the area deflected wide, while Rosicky found himself in a great position, but Dunne again positioned himself well to block.
City then applied the pressure, firstly when Petrov flashed a shot wide of the far post after cutting in from the left.
Eriksson and his bench were off their feet claiming a penalty when Johnson was flattened by Toure in the area, but Foy waved play on.
Then after 62 minutes Mpenza raced through, but Almunia spread himself to deny the striker.
They were almost made to rue their misses when Richards brought down Alexander Hleb in the area and the assistant referee instructed Foy to point to the spot.
However, Schmeichel saved with his legs as Van Persie blasted down the middle and he denied the striker again two minutes later with a long-range effort.
The City keeper then tipped Fabregas' powerful effort over the bar.
But the Spaniard was not to be denied with 10 minutes remaining.
The ball was fed to Hleb on the right before he slipped a pass Fabregas, who smashed into the roof of the net at the near post.
Schmeichel forced Almunia into a stoppage-time save when he raced up for a corner.
Sven upbeat after first lossDespite tasting defeat for the first time as a club manager in England,
Sven Goran-Eriksson was pleased his side caused Arsenal problems, with Martin Petrov, Elano
and Emile Mpenza all guilty of wasting first-half opportunities.'It is tough to lose but I think we played better than against Manchester
United,' said Eriksson. 'I am rather happy: we worked hard, we stood up to
Arsenal when they moved the ball around, as they are famous for, but we also
played some good football.'In the second half, Petrov flashed a shot across the face of the goal and
Manuel Almunia, deputising for Jens Lehmann, rushed out to deny Mpenza when the
City striker was sent through.For all of Arsenal's possession, Richard Dunne and Micah Richards combined at
the heart of City's defence to frustrate the hosts, the only mistake from
Richards coming in the 66th minute when he brought down Alexander Hleb.Schmeichel denied Van Persie with his legs before Fabregas lashed in with 10
minutes remaining. While Eriksson is looking to bolster his squad with a
striker, Schmeichel's form means he is not in the market for a goalkeeper.'After I saw Schmeichel the first time, I said that we would only get a new
goalkeeper if we found a new Petr Cech or someone like that,' said the City
boss.'The way he is playing at the moment, we could ask no more from him. I don't
think he could do much about the goal, he saved the penalty and even though he
is not the biggest keeper, he has a presence you can feel from the bench. He is
very brave as well.'Eriksson's other young talent is Richards, who continued on from his
impressive form for England in midweek.'He is solid, like a rock, and very dependable, He just has to keep his feet
on the ground because he has everything you could ask for,' said Eriksson.Arsenal boss Arsene Wenger lost Philippe Senderos (ankle) in the warm-up and
Bacary Sagna (back) in the first half.After late wins against Fulham and Sparta Prague, the Frenchman was delighted
with another example of his side fighting until the end.'I was worried a bit but the side is ready to fight until the last second.
The defenders had a lot of work to do and they did it very well,' he said.'Eventually Fabregas came through and the midfield is getting goals now. We
won with style, against a good side and we defended very well. 'We created
chances but even when things didn't go for us we kept going.'We won in the last seconds at Fulham, we scored a second goal at Prague in
the dying moments, we missed a penalty and still won the game here. That is a
recognition of what is going on in this team and how we are progressing.'Schmeichel's father Peter famously saved against Arsenal in 1999, with
Manchester United going on to complete a treble, and Wenger added: 'The penalty
flashed in 1999 - Bergkamp versus Schmeichel - through my mind. I hoped history
wouldn't repeat but it happened again - let's hope we don't meet his
grandson!'Meanwhile, Wenger admitted it is unlikely that there would be fresh faces in
his squad before the transfer window closes, adding: 'I am not in the market
for any new players.'
Arsenal 1 - 0 Manchester City
