 Eastham made his Arsenal debut against Bolton Wanderers on 10 December 1960, and scored twice as Arsenal won 5–1.Later on that same season, he scored the equaliser against his former club Newcastle United at St James' Park, in a 3–3 draw, during which he was called "Judas" and pelted with apples.Throughout his six seasons at Arsenal, he was a regular for the side; though not a prolific goalscorer, Eastham was one of the most talented players of what was an average Arsenal side at the time; under George Swindin and Billy Wright, Arsenal never finished higher than 7th during his time there.