Palace's tally of nine points from their first 13 matches represents their worst start to a Premier League season in six years, but boss Oliver Glasner will hope Munoz's late equaliser will give his side the lift they need to haul themselves further away from relegation danger.
Despite being by far the better side against a toothless Newcastle, it looked as though the Eagles' lack of cutting edge would come back to haunt them as they racked up 16 shots without breaching the visiting backline.
After Sarr was denied by a fine Pope save, Munoz should have done much better from the Senegal international's low ball.
Newcastle's opener came out of nothing but apart from Burn's block to thwart Munoz, Palace looked unlikely to add to their miserly tally of three home league goals in 2024-25 until the Colombian's first for the club since his January arrival from Genk.
Glasner's team have now picked up three draws from their last four games in the top flight, but their inability to finish clear-cut opportunities - particularly at Selhurst Park - remains a concern.
"We have to blame ourselves that we didn't take those chances," Glasner, who sprinted down the touchline to celebrate Munoz's equaliser with his players, told BBC Match of the Day. "With Newcastle's pace in attack, you always have to take care that you don't get [hit on] transition situations. Everyone deserved the equaliser.
"We feel we deserve a bit more [this season]. It's not that we miss [chances] because we're arrogant. It's about how you deal with it. What gives me a lot of confidence is the character of the players here at Crystal Palace.
"It's frustrating, but on the other side we know we'll come through it together. The way we're playing is improving game-by-game, and then the results will come."
Palace return to action in a crunch game against Ipswich on Tuesday, before hosting Manchester City next Saturday.