Teenager Aarons looked to have inspired Newcastle to a first win of the season after coming off the bench to score one and create another until Zaha pounced five minutes into added time to make an immediate impact following his return to Palace on loan from Manchester United.
Palace enjoyed a flying start to the match and were in front inside the opening minute when Dwight Gayle reacted the quickest to turn home the loose ball after Marouane Chamakh’s shot had been pushed onto the post by Tim Krul.
Newcastle levelled eight minutes before half-time when Darryl Janmaat fired home his first goal for the club at the second attempt after the ball had bounced around the penalty area.
But Palace regained the lead three minutes into the second half when Jason Puncheon’s driven volley took a slight deflection on its way past Krul.
Alan Pardew’s side came back again on 73 minutes when Aarons, who had only been on the pitch six minutes, guided a header into the net for his first goal for Newcastle.
Zaha, who could have scored before Newcastle equalised, thought he had immediately restored Palace’s advantage, but the substitute was ruled offside.
With two minutes to go, Aarons cut in from the left and his curled ball into the area came back off the far post and Williamson tucked the ball home from a couple of yards out.
Deep into stoppage time, Palace pinched a point when a free-kick was launched into the box and the ball dropped for Zaha to rifle a low shot through a crowd of bodies.
Having failed to score in either of their first two league games and won in the Capital One Cup at Gillingham by virtue of John Egan's own goal, Alan Pardew knew victory against Palace was a must if he was to convince the club's fans that his new-look side have enough attacking threat.
But whatever his game-plans was, it was blown out of the water within 30 seconds as Gayle handed Warnock the perfect start to his reign, pouncing on the rebound after goalkeeper Krul could only turn Chamakh's shot on to a post and blasting into the roof of the net.
The visitors, who were also looking for their first three-point haul of the campaign, predictably retreated deep inside their own half as the shocked Magpies started the process of fighting their way back into the game.
In a frustrating passage of play, the home side dominated possession, but simply could not find a cutting edge as lone striker Emmanuel Riviere was well-marshalled by the Palace rearguard, which repelled a series of insipid set-piece deliveries from Remy Cabella and Jack Colback with little difficulty.
Warnock's men might have increased their lead when the recalled Puncheon, whose infamous spat with his new manager appeared to have been forgotten, fired just over after a rare break.
However, as the half wore on, Newcastle started to make an impression, with Janmaat heading wide from a Cabella corner and Moussa Sissoko drilling inches past a post after enterprising set-up play by Siem de Jong and Riviere.
But the equaliser finally arrived eight minutes before the break from an unexpected source, and courtesy of a slice of good fortune.
Riviere laid off Cabella's ball into the box and it eventually fell to Janmaat, whose initial effort pinballed between defenders before the ball sat up nicely for him to stab past keeper Speroni with the help of a deflection off defender Damien Delaney.
The Magpies had an opportunity to go in ahead at the break when Cabella squared a free-kick to Colback on the stroke of half-time, but the midfielder failed to celebrate his call-up to the England squad in style when he spooned his effort high over.
There is little doubt Pardew will have exhorted his troops to raise the tempo on their return, but in the event, they started just as sloppily and were made to pay once again.
Yannick Bolasie was allowed to pick up possession wide on the left and square for Puncheon, who controlled neatly before sending a volley across Krul and into the far corner.
Newcastle were almost caught out once again with 57 minutes gone when full-back Martin Kelly exploited the space left by opposite number Janmaat as he pushed forward to surge down the left before cutting inside and testing Krul from distance with a rasping drive.
But it took a good save by Speroni to deny Yoan Gouffran a 62nd-minute equaliser after De Jong had combined with Riviere to allow Colback to feed the Frenchman.
Pardew introduced Aarons in a bid to add much-needed invention, but it was fellow newcomer Zaha who almost extended his side's lead 18 minutes from time when he waltzed through the home defence before seeing his effort blocked by Krul.
But Aarons did make a swift impact two minutes later when he stooped to head home a second equaliser at the far post after Cabella's left-wing corner had been flicked on.
Zaha was proving to be a serious nuisance and he perhaps should have scored nine minutes from time when he blazed wide of the far post after Krul had parried his first attempt.
Williamson must have thought he had won it when he tapped home from close range after Aarons' audacious effort had come back off a post, but Zaha finally got it right to ensure it finished all square.
Phil Thompson on Newcastle v Crystal Palace
"Neil Warnock went up to Mike Jones, the referee, after the game and was absolutely delighted. He was shaking his hand. I thought if it had finished five minutes earlier, before they’d scored, he’d have been shaking his neck!
"This was a great game with both sides going for it. Newcastle had all the possession and were trying to break Palace down, but De Jong and Riviere weren’t able to open them up. However, I look at Aarons and he’s got pace, he’s got ability, he leaps for fun and this boy is a real talent. He can excite you, but he does it in the right areas. It was a fantastic game and an absolute delight to watch."