Sam Allardyce's side took an early lead through the left-back's sublime free-kick but the Austria international found an equaliser deep in injury time
Aaron Cresswell opened the scoring with a stunning free-kick in the seventh minute but Arnautovic, who already had two efforts ruled out for offside, found the net moments before the final whistle to end Stoke's three-game run of defeats.
The draw leaves both sides on 43 points in the Premier League, with West Ham in ninth and Stoke City a place below.
Stoke made a sluggish start and it was quickly punished by the hosts. Glenn Whelan bundled Enner Valencia to the floor 25 yards from goal, leaving Cresswell to step up and whip a superb strike beyond Asmir Begovic and into the top corner.
Cheikhou Kouyate sauntered past a pitiful challenge from Steven N'Zonzi to test the Stoke goalkeeper in the 16th minute, although Winston Reid was forced into a last-ditch block to deny Jonathan Walters as Stoke belatedly stirred.
Mark Hughes' men were carrying the greater attacking threat by the time Jonathan Walters cut in from the left to ripple the side netting and home goalkeeper Adrian turned a Victor Moses snapshot behind six minutes before the break.
But the on-loan Chelsea forward endured an early end to his afternoon, injuring his left knee when he sent another shot narrowly wide in the closing moments of the half.
That brought Mame Biram Diouf into the action and, early in the second half, Stoke full-back Erik Pieters came on as Marc Wilson hobbled from the field.
The next enforced change was for West Ham, with Carlton Cole replacing the injured Diafra Sakho before the hour, and the stoppages went a long way to explaining an uneventful and disjointed start to the second half.
Charlie Adam dragged wide from the edge of the area under pressure from James Collins before the midfielder - who scored a stunning goal from the halfway line in last weekend's loss to Chelsea - picked out Arnautovic to slot home a tidy finish from an offside position.
West Ham's sharpness in attack diminished in Sakho's absence, but Kouyate found space in the box after 71 minutes and forced Begovic to beat a low strike out of the bottom corner.
At the other end, Adrian found himself comfortably beaten when he gratefully saw Diouf's well-directed effort cannon back off the upright.
Arnautovic cut a furious figure when the assistant's flag curtailed his celebrations for converting substitute Stephen Ireland's pass, but he finally found the equaliser in the fifth and final minute of added time.
The Austria international drove purposefully at a tiring West Ham defence and lashed into the bottom left-hand corner.