Liverpool came close to grabbing the opening goal as Jordan Henderson was allowed to run into the Arsenal penalty box, although he then failed to connect with his shot.
The Gunners opened the scoring with 18 minutes gone through Cazorla. The Spaniard headed a cross against the post but raced on to the rebound to slam home.
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Mignolet was called into action again, pushing away Aaron Ramsey's shot from the edge of the box.
Daniel Sturridge showed good skill to evade the Arsenal defence, but eventually ran the ball out of play.
Cazorla then fired wide of the post towards the end of the first half.