Eastham was purchased by Stoke City manager, Tony Waddington, for a fee of £35,000, prior to the start of the 1966–67 season. Eastham spent the next eight seasons at Stoke City, during which the club maintained their status in the First Division. He played in a side which combined home grown talent – such as the likes of Denis Smith, Eric Skeels and Mike Pejic — alongside the experience of veterans like Eastham and Peter Dobing. Stoke won the League Cup in 1971–72, with Eastham scoring the winning goal in the final against Chelsea, which finished 2–1. At the age of 35 years 161 days, he became the oldest player to receive a winner's medal. He was also a beaten FA Cup semi-finalist in successive seasons (1970–71 and 1971–72) — both times in replays and both times by his former club Arsenal. Eastham also represented Stoke at European level, playing in the 1972–73 UEFA Cup; the first time the club had competed at European level in its history. In the first round, Stoke played Kaiserslautern of Germany but lost 5–3 on aggregate over two legs and were knocked out of the competition in the process.