The defeat for Arne Slot makes it Liverpool’s ninth defeat of the season as they sit fifth in the league standings.
Tomas Soucek pulled one back for West Ham in the 49th minute when he guided home Malick Diouf’s pass from close range.
The Blues currently sit fourth on the table with 45 points.
Antoine Semenyo opened the scoring for the hosts in the 24th minute.
Wilshere succeeds Matt Bloomfield, who was sacked earlier this month after less than a year in charge at Kenilworth Road.
Arsenal moved second on the league standings after the Gunners secured a dominant 5-2 away win against West Ham United in their Premier League tie at the London Stadium on Saturday
Manchester City suffered a shock 2-1 defeat at Bournemouth on Saturday, ending their 32-game unbeaten run in the Premier League.
The summer transfer window has seen a record 11,000 players around the world join new clubs in men’s football, with $6.46 billion spent.
It was the former Liverpool goalkeeper’s first Premier League start since 2018.
The Red Devils eventually picked up the three points which took their season’s tally to 69 points.
