Palace were then denied a 12th minute penalty, when Sako appeared to be upended by James Tarkowski, although the defender did get a toe to the ball.
From a similar position in the 21st minute he gave Palace the lead.
A second goal in two games from Bakary Sako was enough to secure the three points for the Eagles that would take the hosts up to 12th, and into serious contention for a top-10 finish having looked like near-certainties for relegation a few weeks ago.
That poisoned chalice might one day pass to Sean Dyche, who has rarely seen his robust backline endure as many problems as Sako, Christian Benteke and Wilfried Zaha inflicted during the opening half hour.
There was still plenty to do when Sako retrieved Benteke's flick, but he drove towards a backpedalling Phil Bardsley and crashed a low shot through Tarkowski's legs that flew into the net via the boot of Nick Pope.
They were fortunate to escape further punishment when Charlie Taylor's weak header was intercepted by Zaha and it required a brilliant last-ditch clearance by Ben Mee to prevent James McArthur from converting.
A Sean Dyche rollicking at the break inspired the Clarets as they searched in vain for a goal with Sam Vokes nodding into the side-netting.
Burnley had to wait until the 36th minute to have a true sight of goal when Vokes glanced a header wide of the upright once the ball had been recycled back out to Johann Berg Gudmundsson on the left.
Benteke had a chance and Sako went closer still on the stroke of half-time.
The Canadian Arfield has just six months left on his current deal and he has reportedly attracted interest from the Hammers as well as Brighton and Crystal Palace.
Crystal Palace continued their excellent form in the Premier League with a 1-0 win at home to Burnley.
According to the official Crystal Palace website, Timothy said: "I have enjoyed my time here and it's a great opportunity to play in the Premier League and has been a good experience for me".