He became a regular in the Stoke squad in 1969–70 and the early seasons in the 1970s. Stoke enjoyed a successful period, reaching the semi-final of the FA Cup twice and winning their first major trophy – the League Cup – in 1972. He played the whole ninety minutes of the final, as the "Potters" beat Chelsea 2–1 at Wembley thanks to goals from Terry Conroy and George Eastham. During two seasons, 1970–71 and 1971–72, Pejic played in over 100 senior matches. He earned a call up to the England national side in 1974, playing in four matches, but lost his place to Liverpool's Alec Lindsay. During his time at Stoke Pejic was prone to being sent-off and was once suspended for five matches by the FA. He broke his leg in February 1975, and injuries to three other key players caused Stoke's bid for the First Division title in 1974–75 to fall away to a fifth-place finish. In January 1976, the Butler Street stand roof at the Victoria Ground collapsed after a powerful storm gripped the area. To cover the costs the club had to sell their most valuable players and Pejic joined Everton for £135,000.