West Ham turned over Stoke a few months ago.
However, Carroll - who earns £90,000-a-week at the London Stadium, according to Spotrac - ensured that the points would be shared and the Irons would extend the daylight between themselves and the bottom three.
It couldn't have come at a worse time with national team boss Gareth Southgate watching from the stands in east London.
Pablo Zabaleta ran behind the defence and squared for Arnautovic, who shot straight at a starring Butland, before Mario missed an absolute sitter from a cross into the middle. We had good moments, good chances and we've been playing well.
First, Marko Arnautovic converted Aaron Cresswell's cross with a deft header but he had strayed marginally offside. Paul Lambert sank to his knees inside his technical area. I've never really had a problem lifting them - they have been a credit to the club, doing everything to stay in the league.
The home side thought for a second time they had taken the lead, only for the linesman's flag to once again deny them.
Mame Biram Diouf then tested Hart with a powerful strike down the other end of the field, before Butland made a brilliant save to keep out a close-range Arnautovic attempt 10 minutes before the break.
Lambert responded by throwing on Crouch to replace Bauer and, with just under 15 minutes remaining, Moyes sent on Hernandez to a big cheer from the home crowd.
Carrol came on in the 96th minute of the game v Stoke and made an almost-instant impact.
A late Andy Carroll goal meant it didn't prove too costly as the Stoke clash finished 1-1 but the mistake was the latest of a long list for Hart.
The 37-year-old former England worldwide loitered in the penalty box and managed to beat the current England player to the ball after Hart had allowed Xherdan Shaqiri's reasonably tame shot to slip from his grasp.
Shaqiri pointed to the West Ham result as a fitting summary of the season as a whole, with the club now facing the serious prospect of dropping into the Championship.