Greaves scored five goals in a 6–2 win against league champions Wolverhampton Wanderers in the third match of the 1958–59 season. Chelsea remained inconsistent, though despite his team finishing in 14th place Greaves managed to finish as the division's top scorer with 32 goals in 44 league games. Greaves scored 29 goals in 40 league matches in the 1959–60 campaign, five of which came in a 5–4 victory over Preston North End. Despite his goalscoring exploits, the club could manage only an 18th-place finish, three places and three points above the relegation zone.