The Clarets were second best for the majority of the game but goals from Jeffrey Schlupp and an own goal from Luka Milivojevic settled proceedings.
Burnley looked tired at many points during the game after their third game in a week and will look to freshen up quickly with a home game against Leicester City just around the corner.
Michael Olise - A star in the making?
The young Frenchman was by far the best player on the pitch for Crystal Palace today and caused Burnley no end of trouble.
The former Reading man set up Schlupp for Palace's goal in the first 10 minutes after he twisted and turned before firing the ball across goal for the former Leicester man to stab past Nick Pope.
This was just the start of Olise's impressive afternoon as he had the better of both Erik Pieters in the first half but also the returning Charlie Taylor in the second half after he replaced the injured Pieters.
The Eagles had far the better of proceedings on the day and may feel a little disappointed that they didn't come out with all three points.
A slow start to the second half cost Palace but Viera will be pleased that his young squad is showing bags of potential especially in the form of Olise.
Burnley look a little lethargic
Many Burnley fans won't be disappointed by a good point on the road to cap off a crucial week in their battle for survival.
What may bother Sean Dyche though is that the side's performance today seemed a little lethargic, probably due to the fact that they've played three times this week.
The Clarets were nowhere really to be seen in the first half and looked very slow after back to back wins over Brighton and Tottenham respectively.
Dyche obviously rattled the troops at Half Time as just 45 seconds after the break, Luka Milivojevic put the ball into his own net after good work from Jay Rodriguez and a rejuvenated Aaron Lennon.
In a week where The Clarets took seven points from a possible nine, there is certainly reasons to believe that Burnley are up for the relegation dogfight.
Saturday's performance was definitely not Burnley's best but a point on the road is a positive and something to take into the next game.
The battle at the bottom intensifies
Everyone talk about the race for the title this season but the battle to stay in the division is just as intense this season.
There is potentially a number of sides that are in trouble and all with varying degrees of form to show.
Newcastle United have certainly shown that their winter investments have paid off as they look to be dragging themselves away from danger.
Sean Dyche's side will be hoping that their strong current momentum can boost themselves up the division and with games against all of the bottom six bar Leeds still to come, it could get very tasty indeed.
Dyche certainly knows how to get his side out of trouble but with Burnley and Newcastle on the rise and Leeds, Brentford and even Everton in serious trouble, it is almost impossible to call what will happen come May when the season draws to a close.
It may well end up being the closest ever at the bottom with seven or eight teams still in trouble but it's now or never for some and the evidence is showing that some want it more than others.