The Gunners secured three points to top the league table.
Both teams went into the break without scoring. But Leandro Trossard broke the deadlock for Arsenal in the second half.
Wilshere succeeds Matt Bloomfield, who was sacked earlier this month after less than a year in charge at Kenilworth Road.
Manchester City struck first just nine minutes into the first half with a goal from Erling Haaland.
Real Madrid hosted French side Olympique Marseille, with Xabi Alonso avoiding a debut defeat thanks to Kylian Mbappé.
Recent league matches at Anfield have mostly ended in stalemates, including a 2‑2 draw in May 2025 when Arsenal came from two down.
Eze was unveiled as the new No. 10 after completing a deal worth over £60 million from Crystal Palace.
The Gunners’ offer came after attacker Kai Havertz suffered a knee injury.
Arsenal weathered the storm and tightened their grip in the closing stages.
Ziegler pointed out that social media continues to be the main hotspot for these scams.
