United went 2-0 down with goals from Kirsty Howay and Molly Sharpe firing the Eagles into a commanding lead after dominating the majority of the game.
However, with a raft of changes from Becky Langley in response to going behind, United found a way back into the match. Firstly, it was Oona Sevenius who calmly finished beneath the diving Shae Yanez from close range.
Then, with the game ticking over into the 98th minute, Gautrat fizzed in a wicked corner from the right, which caught out the Palace keeper and, despite entering a sea of bodies, found the back of the net.
Only seconds later, the USA international looked to have won an unlikely three points when Emily Murphy's cross found her unmarked, but the Eagles goalkeeper Yanez pulled off an incredible diving save to deny her.
In a first half which lacked clear-cut chances, it was a shot that didn't hit the back of the net which had the Palace fans on their feet.
A punch from Femke Liefting reached the corner of the United box and the feet of Elise Hughes, who volleyed goal-bound but her effort bounced behind, despite some Palace supporters celebrating what they believed to be a goal.
It was just before the half-hour mark when Newcastle got themselves into the game with Beth Lumsden standing up her defender in the box before cutting the ball back to Lia Cataldo.
United's number 99 took aim, looking for her first goal in black and white, but her wait must go on as her effort kissed the far post and went behind.
The wind was a factor for both sides during the first half and almost benefited Palace when Ashleigh Weerden's cross was blown towards goal and bounced off the top of the bar and behind.
As the game approached the final ten minutes of the first half, Freya Gregory stole the ball on the edge of the area, but her deflected shot floated into the hands of Yanez.
It was the hosts who took the lead through Howat. Palace whipped in the ball from the right and managed to recycle the ball and eventually pick out Howat.
Her header bounced in the six-yard box before evading several United bodies and hitting Aoife Mannion on the line, but the Republic of Ireland international could do little to stop the ball crossing the line.
Just seven minutes after entering the match, substitute Murphy was slipped through on goal by Gautrat, but from a difficult angle, United's number 35 slipped her effort wide of the far post.
Sharpe added a second for the Eagles after being on the pitch for just two minutes when the ball was cut back to her ten yards from goal and she curled an effort into the top corner.
Second-half substitute Molly Pike showed her pace down the wing to drive at the Palace defence and set up Nobbs on the edge of the area, but her floated effort sailed over.
Newcastle refused to go away quietly, however, when Sevenius swept home her first goal for the club.
Gautrat worked some space for herself on the right-hand side of the box and looked to have picked out Murphy, but she dummied the ball for Sevenius, who made no mistake in finishing beneath Yanez.
After what looked to be a disappointing trip to the capital, Gautrat's corner directly found the back of the net, catching out Yanez, who made a late attempt to stop the ball.
With her appetite for goals whetted, Gautrat had a chance in the final seconds of added time to win the game. Murphy's elegant cross found her unmarked in the six-yard box, but despite moving the wrong way, Yanez stretched to claw the ball away and secure a point for the Eagles.
Newcastle United Women: Femke Liefting, Lia Cataldo, Aoife Mannion, Deanna Cooper, Demi Stokes (c), Morgan Gautrat, Jasmine McQuade (Lois Joel 61), Jordan Nobbs, Beth Lumsden (Oona Sevenius 75), Shania Hayles (Emily Murphy 61), Freya Gregory (Molly Pike 75)
Subs not used: Claudia Moan, Charlotte Wardlaw, Elysia Boddy, Malgorzata Grec, Jorja Fox
