Here is the second of our three-part guide to Premier League action in the capital. If you fancy booking tickets to see one of the sides in action, log on to the official club sites and book tickets today.
The Eagles have already had a season that fans are never likely to forget, following their surprise promotion in 2013.
Manager Ian Holloway left the team in a miserable state late last year, sitting bottom of the table and with seemingly no hope of surviving.
But things have turned around miraculously in the last few months, in large part because of the influence of new boss Tony Pulis, who has helped to instill a renewed sense of discipline and belief in the side.
In recent weeks, in fact, they have been one of the form sides in the league and there is a growing sense that they can escape the drop - which will come as a shock to most critics.
Palace currently sit 16th in the table and with just over ten games to go, will be hoping to go on a mini-run that will lift them even further away from the relegation zone.
Reflecting on the recent defeat at home to Manchester United and looking ahead to the rest of the campaign, Pulis said: "We’ve got a very difficult run of games at home, so we’ve got to pick up some points against the top teams. They got a break – if we’d have got a penalty and gone 1-0 up, it might have been a different game.
"They got that break and fair play to them."
The Cottagers have also endured a turbulent season, going through two managers and flirting with relegation.
Currently, they sit at the bottom of the table and losing their Premier League status remains a very real possibility.
For this reason, they have recently installed German Felix Magath to the position, in the hope that his disciplined approach will bring about a change in the team's fortunes.
But according to midfielder Lewis Holtby, the new manager is simply determined to get the most from his squad - and this strategy has born fruit so far during his career.
"We all talked about what could maybe happen and that training is going to be very hard," he said. "You have to be honest about that. But the most important thing is to be physically and mentally on the top level.
"Of course he trains hard but everyone has his own philosophy. He won a couple of titles in Germany [two with Bayern Munich and one with Wolfsburg], you always have to respect that."
In order to lift themselves off the foot of the table, the team will need to improve their form dramatically.
The next few games could be decisive in determining the team's fate, but they will be hopeful that the influence of Magath starts to take effect.
It remains to be seen, though, whether both London clubs are able to survive the drop.