Jose Mourinho's men left the Stadium of Light with a 0-0 draw - the first time they have failed to score this season - on Saturday evening as the Black Cats turned in a stubborn defensive display and might even have snatched victory in a late flurry of activity.
City will follow in their footsteps on Wednesday night when they head for Wearside desperate to end a run of four successive 1-0 league defeats on Wearside, although Brown is looking for more of the same.
Asked if Sunderland could extend their remarkable run, the former Manchester United defender said: "After this result, there's always a possibility.
"Every game, we go into the game looking to win it and if we show the same commitment again, I'm sure we'll have chances.
"If you ask any player which teams they want to play, they'd say the top four or five
I suppose you would be up for it a little bit more and wanting to do really well.
"Everyone is watching and why not play well against the best teams?"
Chelsea arrived in the north east six points clear at the top of the league after a 19-game unbeaten start to the campaign and determined not to allow their hosts a third win on the trot over them inside 12 months.
They enjoyed the greater share of the possession, but were rarely able to break through a red and white wall, and although Willian struck a post with a 17th-minute shot, Black Cats defender Santiago Vergini was later denied by the crossbar.
Mourinho, who saw striker Diego Costa pick up just a single yellow card - his fifth of the season, which means he will miss Wednesday game against Tottenham - after clashes with central defenders John O'Shea and Brown, was complimentary about Sunderland's defensive resilience and insisted he had nothing for which to reproach his players.
Brown said: "We made it very difficult
I thought Catts [midfielder Lee Cattermole] was tremendous, like most of the lads, and that gave us a good balance and we showed them they were not going to have it all their own way.
"It helped us
We went in at half-time 0-0 and in the second half, anything can happen
There were a few tired legs, and they had some good chances as well - not perfect chances, but they had a couple of half-chances and then at the end, we probably could have nicked it as well.
"At the beginning of the game, you would have said it would have been a great point earned, but we battled all the way through and then we had a couple of half-chances at the end.
"We are happy with the result
We maybe could have nicked it, but it was a good Chelsea team and we put everything in and managed to stop them scoring and get the draw."
That draw means Sunderland are now unbeaten in four games since their season took an alarming dip with an 8-0 defeat at Southampton and Arsenal's 2-0 victory on Wearside, although Brown insists engineering the transformation has not been complicated.
He said: "If anything, it's just back to basics, doing everything right, not necessarily making it difficult for ourselves, playing simple football, but in a quick way and defending how we know we can defend, where we make it very difficult for teams to score."
Source : PA
Source: PA