Young Spanish defender Hector Bellerin opened the scoring for the Gunners before Ozil and Sanchez added another two within eight minutes to give Arsenal an unassailable 3-0 lead at half time.
Liverpool earned a penalty – which Jordan Henderson duly converted – in the closing stages of the game when Sterling was fouled in the box by Bellerin.
In the extra time, Olivier Giroud scored a beauty after cutting inside and striking with his favourite left foot into the far corner.
Liverpool now trail the Gunners by nine points, and their hopes of making the top four are as good as over.
Check the Live Commentary as it happened.
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