But another substitute would yet have a decisive impact on the result, Carroll superbly turning in a cross from Aaron Cresswell to ensure the spoils were shared at London Stadium.
Coverage of today's Premier League game between West Ham and Stoke City will be shown live on Sky Sports Main Event (Sky channel 401, Sky HD 435, Virgin channel 511) and Sky Sports Premier League (Sky channel 402, Sky HD 436, Virgin channel 512).
Ramadan Sobhi and Moritz Bauer had early efforts saved easily by Hart as Stoke showed plenty of attacking ambition in the opening exchanges.
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 flawless position to block the effort with his face. "I'm pleased with the team's performance, I thought we played well".
Diouf then missed Stoke's clearest chance, turning a Bauer pullback over the crossbar with a first-time strike that wasted a unsafe break.
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Police have warned social media trolls they could be committing a criminal offence by abusing referee Michael Oliver and his wife Lucy. However, his goal had taken West Ham one more step away from danger.
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.
The Hammers were denied by the linesman's flag moments later when fellow substitute Javier Hernandez struck the ball past Jack Butland, but Carroll was adjudged to have handled inside the area.
The point left West Ham seven points clear of the relegation zone. I've just thought about staying in the league and that is still my aim.
"You need a little bit of luck at certain times but the performances have been incredibly high and the way we have played I couldn't ask for any more from the team".
The Potters are unbeaten in their last five league visits to face West Ham, although four of those matches were draws.