A late Julian Speroni penalty save ensured that Palace came out of an entertaining encounter with Burnley with a point after he denied Scott Arfield from the spot with six minutes remaining.
Despite not finding the all-important goal, Palace threatened throughout and went close early on when Scott Dann rattled the crossbar and spurned numerous opportunities during the opening hour, but after that the visitors got a foothold in the game and threatened to steal their first win of the season but found Speroni in inspired form.
Having scored three times against Newcastle United last time out, Palace looked hungry to continue to find the net in the early stages of the game, but it was both of their centre-backs that went closest eight minutes in. Firstly a Jason Puncheon short-corner found Wilfired Zaha in the area and he fed Damien Delaney who saw a goalbound shot deflected over the bar.
Puncheon played the resulting corner into the area and after it was poorly cleared, Fraizer Campbell had the chance to put a second cross into the box which Dann raced onto but saw his header flick the crossbar and bounce clear.
Three minutes later and the Selhurst faithful got their first glimpse of Zaha in full flow. After he was found in space on the left he took on Kieran Trippier and cut inside before firing at Tom Heaton, and after the keeper had parried that away Jason Shackell had to be alert to clear off his own line after the ball ricocheted off him.
After a frantic start the game began began to settle into a more-familiar rhythm but the chances still kept coming for both sides. Scott Arfield smacked a close-range volley well wide into the Holmesdale Road Stand before Puncheon skidded a low effort straight at Heaton.
But midway through the half a glorious chance fell to the feet of Dwight Gayle when James McArthur played a long ball forward and it was poorly headed away by the Burnley defence, but after doing well to take the ball down the red-hot striker fired the ball over the crossbar despite having time to compose himself.
Palace went into the break having enjoyed the majority of the first-half's chances and they continued to fall their way after the restart. Gayle was inches away from turning in Mile Jedinak's knock-down but saw the deflected cross flash wide of the post, and then Delaney rippled the side-netting from another dangerous Puncheon delivery.
Heaton's goal was under constant threat and Puncheon was next to try his luck when he fired wide of the mark from inside the box, and McArthur went close to a debut goal in stunning style with a blast from 25 yards which just drifted.
But with the game still level Burnley were right in it and Speroni was forced into his first save after 63 minutes when Arfield took aim from 25 yards and the Argentinian was forced to push the ball over the bar, and then five minutes later the Scot linked up with Marvin Sordell who laid the ball off to David Jones who should have troubled Speroni more with his 20 yarder.
The tide was beginning to turn and Arfield should have hit the target after Kieran Trippier's free-kick was blocked but the full back neatly played in the Clarets midfielder who blazed over, but substitute Jonny Williams toe-poked another chance wide with 15 minutes remaining to continue to show the Eagles' attacking threat.
But in the 84th minute Sean Dyche's men were handed a golden chance to win the game when Jedinak tussled with Lukas Jutkiewicz in the area at a free-kick and hauled the striker down. After being awarded the penalty, Arfield stepped up but saw a good penalty matched by a brilliant save by Speroni who strongly pushed the ball away one-handed to keep his clean sheet in tact.
Palace: Speroni, Ward, Delaney, Dann, Mariappa, Jedinak (c), McArthur, Puncheon, Zaha (Bolasie 70), Campbell (Doyle 61), Gayle (Williams 73). Subs: Hennessey, Fryers, Kelly, Ledley, Ledley.
Burnley; Heaton, Trippier, Duff Shackell (c), Mee, Arfield, Marney, Jones, Boyd, Jutkiewicz, Ings (Sordell 42). Subs: Gilks, Reid, Ward, Wallace, Long, Barnes.