The Gunners lost both their meetings with Chelsea and Manchester United last season and were again beaten by Carlo Ancelotti's Blues at Stamford Bridge earlier this month.
However, they climbed to second in the table on Sunday following a 3-0 victory away to City, who were reduced to 10 men when Dedryck Boyata was sent off in the opening five minutes.
Fabianski admits the result has given Arsenal a huge lift and fuelled belief that they can go on to enjoy a successful campaign.
"It is a really important win for us because we were behind City in the league," said the Polish goalkeeper.
"Now we are second and in touch with the leading team, Chelsea.
"And, performance-wise, we played really well away from home and won 3-0, so yeah, it's a very, very good win for us.
"I think within the team there was always big belief, but it was still important for us to win a big game like this.
"This season against Chelsea we played well, but didn't win. This game was another big game for us and this time we showed we are capable of winning these games.
"But in the fight for the title it's not only about big games. It's about 38 games and you have to try and win every game."
Fabianski feels Arsenal have the strength in their squad to sustain a title push, but recognises the importance of a cutting edge in attack.
He explained: "We just have to score more goals. We are more ruthless now.
"We are creating chances in every single game and it's not just about making them, it's about taking them.
"We have a big squad of good players and if you look at our squad we have a really strong squad, as strong as anyone's.
"I think we are focused on ourselves. We want to do well this season and fight for the title. That's our aim."
Fabianski produced an impressive performance to help Arsenal shut out City and is satisfied with his form since coming back into the team after being criticised for mistakes in the past.
He said: "I'm just happy that I could help my team and that I could keep a clean sheet for the first time this season. It wasn't really about me.
"I'm happy that we kept a clean sheet as a team because in the last few games we hadn't been able to do that.
"I think we are all pleased with that and keeping a clean sheet helped us get this important win."