Arsenal's Laurent Koscielny and Shkodran Mustafi returned from injury for Arsenal but there was no place in Unai Emery's squad for Mesut Ozil. We played with a mentality of a big team, always going for the second goal.
Alex Iwobi shaved the post with a low shot but Arsenal failed to score for the first time in 21 Premier League matches.
Speaking after the game, Unai Emery admitted that his Arsenal side wasn't good enough in midfield, and said that he was concerned with their form away from the Emirates.
The match was goalless at the interval following near-misses by Arsenal midfielder Matteo Guendouzi and Hammers playmaker Felipe Anderson.
Former Arsenal man Samir Nasri, making his first appearance in the Premier League since 2016, set up the teenage midfielder to wallop home the victor from just inside the box on 48 minutes as West Ham fans celebrated a famous win over their London rivals.
Arsenal were unable to muster a clear cut chance in response, although leading scorer, Pierre Emerick-Aubameyang fired over when he could have done better.
What does it mean?
The defeat in East London was Arsenal's third defeat on the road from their last four games away from home.
Any doubts around Nasri's readiness for Premier League football after so long out will have at least been partially allayed by his performance on Saturday.
Nasri was replaced after 70 minutes - the same time as Arnautovic was removed after a much less impactful display.
Pellegrini refused to delve into whether the Austrian might have played his last game for the club, but confirmed that his substitution was due to a recurrence of the back problem which forced him off in the FA Cup last weekend.