The hosts looked to have done enough to battle to victory after taking an early lead through a superb free-kick by full-back Aaron Creswell.
However, after seeing two efforts from Arnautovic's ruled out for offside and a header by substitute Mame Diouf hit the post, the visitors snatched a point deep into five minutes of stoppage time when the Austrian forward crashed the ball into the far corner.
The Irons had made a flying start as Creswell's superbly struck free-kick gave them the lead after seven minutes
Enner Valencia, back in the side having recovered from a toe injury, was brought down by Glenn Whelan some 25 yards out.
Mark Noble shaped to take the free-kick, but ran over it to instead allow left-back Creswell to strike the dead ball, which flew up over the wall and past Stoke goalkeeper Asmir Begovic into the top right corner.
The early goal had rattled Stoke, looking to move above West Ham into the top 10, as Valencia and Cheikhou Kouyate looked to stretch the visitors defence.
Begovic, who is out of contract in the summer and yet to agree a new deal, got down quickly to smother a low shot from Senegal midfielder Kouyate.
There were plenty of hefty challenges flying in, with the patience of referee Roger East eventually running out on 21 minutes when James Collins clattered into Whelan on the far touchline, and was cautioned.
When Stoke did build a spell of possession, the final delivery into the West Ham penalty area was poor.
Stoke midfielder Charlie Adam, who netted a spectacular goal at Chelsea from his own half last weekend, sent an ambitious 30-yard free-kick high into the Bobby Moore Stand.
Jonathan Walters cut in from the left and slid a low shot towards the near post, the ball ending up in the side netting.
After 43 minutes, Stoke forward Victor Moses, on loan from Chelsea, latched onto a loose ball and fired just wide from the edge of the area, but he fell awkwardly in the challenge and hobbled off with what looked like a knee problem
Senegal striker Mame Diouf came on.
In stoppage time, West Ham broke quickly through Valencia down the right, but Kouyate dragged his shot wide after being played into the Stoke penalty box.
Stoke had to make another change just a few minutes into the second half as full-back Marc Wilson went off, with what looked like a groin problem, to be replaced by Erik Pieters.
Walters continued to offer an outlet, and floated a 25-yard effort just over.
West Ham had gone a bit flat, and manager Sam Allardyce looked to freshen up the attack as Carlton Cole replaced Diafra Sakho before - on 67 minutes - defensive midfielder Alex Song was substituted for Kevin Nolan.
Arnautovic thought he had levelled when collecting a long pass into the area and slotting past Adrian, only for the offside flag to be raised.
At the other end, Kouyate's angled drive was pushed behind.
Stoke went close again on 80 minutes as a header from Diouf crashed back off the inside of the post, bounced across goal and clear.
Cole nodded his header down and wide at the far post as the Hammers looked to close out victory.
Arnautovic thought he had equalised again when converting a cross from Steven Ireland, but again the assistant's flag was up quickly.
However, Stoke were not to be denied as Arnautovic surged forwards, held off the defender at the right edge of the penalty area, before slamming the ball low into the bottom right corner for a share of the spoils.
Source : PA
Source: PA