"That decade might be about to come to an end with Stoke six points off safety with only five games to play".
They did not have too many clear goal-scoring chances with Ramadan Sobhi, Moritz Bauer and Mame Biram Diouf all producing straightforward saves from Joe Hart in the first half.
With the tempo rising, Arnautovic hit the target with a powerful near-post drive only to find Butland in the way, the England goalkeeper in ideal position to block the effort with his face.
The former England global quickly came up with a massive moment for his side, showing attacking instinct to ram home the loose ball after Hart somehow let Shaqiri's strike slip out of his grasp.
Both sides had labored starts to the second half, and West Ham thought they had gone in front but Arnautovic was correctly ruled for offside after sneaking just ahead of the defence.
He said: "It was disappointing for us as we'd had a few other chances and a few goals disallowed".
However, the Hammers hit back at the death as Carroll volleyed Cresswell's low cross into the bottom-left corner of the net from 16 yards out to clinch a draw in the 90th minute.
Javier Hernandez soon rifled home what might have been a Hammers victor, but Carroll had handballed and no goal was given.
The goalkeeper has only just got back in the West Ham team after losing his place to Adrian at the end of November.
Manager Paul Lambert has no further injury concerns to contend with for the trip to the London Stadium.
- This clash produced 36 fouls, a joint-high tally in the Premier League game this season (level with Chelsea v Manchester United on November 5).
Butland didn't know much about Arnautovic's angled shot that struck the Stoke keeper in the face on 36 minutes after Pablo Zabaleta had kept the ball in play on the right, and Arthur Masuaku flashed a long-range effort wide of the right post moments later.
The Hammers are aiming to complete their first league double over Stoke since the Potters' first season in the Premier League in 2008-09.