Laurent Koscielny's equaliser rescued a point for the Gunners after they had blown a two-goal lead during an extraordinary spell either side of half-time.
But Arsene Wenger's side, who realistically needed to win every remaining game to stand a chance of catching leaders Leicester, could find themselves 13 points adrift with just 18 to play for by Sunday evening
They were 2-0 up and seemingly cruising to a third straight victory thanks to goals from Mesut Ozil and Alexis Sanchez
But Carroll, making a rare start in what has been another injury-hit season for the Hammers, turned the game upside down with his first treble since August 2010 for Newcastle, staking a late claim for a place in Roy Hodgson's England squad for Euro 2016
Suddenly West Ham were right back in the race for the Champions League places, only for Koscielny to secure a draw which does little for either side's ambitions this season.
West Ham were already feeling aggrieved after Manuel Lanzini had an early header ruled out for a borderline offside decision
And in the 18th minute they were caught napping by in-form teenager Alex Iwobi, who slid the ball into the area where Ozil had just stayed onside to fire across Adrian
The second goal arrived in the 35th minute, Sanchez starting a slick Arsenal move which culminated in Iwobi lifting the ball over the West Ham defence for the Chile forward to apply the finish
But West Ham piled forward, sensing a goal before half-time would keep the match alive - and they got two in the space of a minute thanks to Carroll.
First the former Liverpool front man got on the end of Aaron Cresswell's cross to power a header in at the far post.
And moments later, in first-half stoppage time, Carroll acrobatically turned in Mark Noble's cross at the second attempt to haul his side level.
Carroll was not finished there, though, and thought he had teed up Dimitri Payet to hit West Ham's third just after the break, only for another goal to be disallowed, this time for a foul on Koscielny.
But in the 52nd minute Carroll completed his hat-trick when he rose at the far post again and nodded Michail Antonio's cross past David Ospina.
Shellshocked Arsenal came close to equalising when Nacho Monreal's shot was cleared off the line by Lanzini.
And they dragged themselves level in the 70th minute when West Ham failed to clear Hector Bellerin's cross and Koscielny produced a smart finish to guide the loose ball home.
With the game becoming stretched and both sides desperate for a win, they traded chances, with Payet close for West Ham and Danny Welbeck and Theo Walcott threatening for the visitors
But point apiece does neither side any favours, with Arsenal's title hopes surely now over and West Ham still finding the top four a bridge too far
TWEET OF THE MATCH
"With Andy Carroll in ya team....don't mess about...put the ball in the box and he will cause havoc
He stays fit then get him on the plane" - former Manchester United defender Rio Ferdinand.
PLAYER RATINGS
West Ham
Adrian: 6/10
James Tomkins: 7
Winston Reid: 7
Angelo Ogbonna: 6
Michail Antonio: 6
Cheikhou Kouyate: 7
Mark Noble: 7
Aaron Cresswell: 6
Manuel Lanzini: 7
Dimitri Payet: 6
Andy Carroll: 8
Substitutes
Emmanuel Emenike (on for Tomkins, 45 mins) : 6
Arsenal
David Ospina: 5
Hector Bellerin: 6
Gabriel: 6
Laurent Koscielny: 7
Nacho Monreal: 6
Mohamed Elneny: 6
Francis Coquelin: 6
Alexis Sanchez: 7
Mesut Ozil: 7
Alex Iwobi: 6
Danny Welbeck: 7
Substitutes
Olivier Giroud (on for Elneny, 67): 6
Theo Walcott (on for Welbeck, 81): 5
Aaron Ramsey (on for Coquelin, 59) : 5
STAR PLAYER
Carroll: The West Ham striker looked like he was up for the game from kick-off and three goals in eight minutes saw turned the match on its head
Carroll was a handful throughout, his power and strength in the air too much for the Arsenal defence
It was a performance to make England boss Roy Hodgson take notice
MOMENT OF THE MATCH
Carroll's two goals in three minutes just before half-time completely changed the game
Arsenal had been the dominant side in the first half, but, with just minutes of the opening 45 minutes left, West Ham struck twice
The former Liverpool striker powered home a header and then struck with an acrobatic effort to put an entirely different complexion on the game.
VIEW FROM THE BENCH
West Ham manager Slaven Bilic made only one substitution throughout the match as he watched his side come from behind
Arsenal manager Arsene Wenger made three second-half changes, including bringing striker Welbeck off for Walcott, who struggled to have an impact.
MOAN OF THE MATCH
The match could have taken a completely different path had Lanzini's early header been allowed to stand instead of being harshly ruled out for offside
It is a decision which is unlikely to have any bearing on Arsenal's title chances, but could have a bearing on West Ham's hopes of making the top four.
WHO'S UP NEXT?
West Ham v Manchester United, FA Cup (Wednesday, April 13)
Arsenal v Crystal Palace, Premier League (Sunday, April 17)
Man-of-the-match Carroll said he had one eye on this summer's European Championships.
He told BT Sport 1: "Without a doubt (I've been thinking about it)
I have to keep that in the back of my head
But at the minute I've just got to play each game here and see how it goes."
On the game itself, the former Newcastle striker added: "It was tough game, we went down 2-0
It was disappointing and in the first half we didn't play our best, but we were lucky to get two goals back just before half-time and come out level after the half.
"It was tough first half, they pressed us
Our set-up didn't suit us and we changed it at half-time, but obviously just before half-time we nicked two goals back which was delightful for us."
On where the draw left the Hammers' top-four hopes, Carroll said: "(I think we're) still in it.
"Obviously we'd have liked the three points, but it was against Arsenal, who are going for the title
It's going to be a tough game, we're happy with the draw I think."
His boss Bilic was pleased with the way his side fought back, but was disappointed not to get maximum points.
He said: "We showed the quality in the first place and the character and team spirit and we came back in a great time - in basically no time
"Then in the second half, of course whenever they were up front, close to the box, they had that capability and class.
"When there is no space they can find the space, but we were better and we had so many chances, or possibilities or situations to kill the game off a little bit, like on 3-2 for us, but we didn't and they equalised and it was very open until the end.
"I'm not happy with (just) a point to be fair, but I'm happy with everything else."
Arsenal manager Wenger admitted the result had hampered his side's title ambitions.
He said: "It makes it much more difficult of course
We have to wait for the results and as well focus on our next game because they are chasing behind us as well.
"We dropped two points today, let's see the results over the weekend."
Source : PA
Source: PA