Arsene Wenger's side started their final visit the Boleyn Ground the brighter of the two with goals from Mesut Ozil and Alexi Sanchez giving them a two goal cushion, but two goals from Carroll brought the Hammers level before the break.
He rounded off his hat trick just after the restart but a goal from Arsenal skipper Laurent Koscielny 20 minutes from the end saw the spoils shared.
Both sides came into this match needing the three points and for a brief moment it looked like the home side had taken a crucial lead as, after 15 minutes, Manuel Lanzini nodded in, but the flag was raised in what at a second glance looked to be a questionable decision.
After that left off, Arsenal took full advantage as they took the lead after 18 minutes. Play carried on after Nacho Monreal appealed for a penalty through Alex Iwobi, who played it into the path of Ozil and he gave Adrian no chance as he coolly slotted home.
They were at it again 10 minutes from the break. It was a great move once more as Danny Welbeck created the space for Iwobi to slot it through to Sanchez, with the Chilean finishing the move in style.
Carroll troubled David Ospina for the first time in the 39th minute and, with a minute of normal time in the first period remaining, he managed to get a goal back.
It was on a plate for the striker after Aaron Cresswell’s superb cross landed on his head perfectly, and he guided home.
The match was then turned on it’s head as Carroll quickly equalised right at the end of the half. It was poor defending on behalf of the visiting side, particularly Gabriel, as they allowed Carroll to have a second bite of the cherry and he made no mistake.
Slaven Bilic’s side were denied another goal just after the restart, and on correct grounds this time, when an initial foul from Carroll on Koscielny saw the flag raised as Dimitri Payet struck home.
It didn't matter much as the home side completed the turnaround in style with Carroll grabbing his hat-trick in the 52nd minute. It was once again a case of poor defending as Michail Antonio was allowed to get to the by-line by Monreal and a simple chip into the area was brilliantly converted as Carroll rose highest to thunder a header past Ospina.
Points snatched away
As the game entered the final 20 minutes, Arsenal began to turn up the intensity and they looked to have equalised as Monreal's 20-yard strike had Adrian beaten, but Lanzini showed great awareness to clear off the line.
However he could do nothing to prevent the away side taking a point just a minute after preventing a certain goal. It was great goal from the Arsenal skipper, Koscielny, as he showed initiative to stay forward after the corner was cleared and was rewarded as he got on the end of Ozil's low cross to grab his fourth goal of the season.
Payet has become a cult hero since his summer move to East London and almost looked like he would enhance his reputation among the Hammers faithful as he curled a effort towards goal in the 72nd minute, but Ospina saved comfortably to see the points shared.