Born in Blagoevgrad, Kostov began his career at Pirin 2001 as an important part of their youth team.

On 25 September 2010, in a home match versus Minyor Pernik, Stanislav scored the only goal for Pirin in a 1–1 draw.

On 16 October he assisted Boris Kondev for the opening goal in a match against Levski Sofia, but Pirin went on to lose the game 4–1.

On 22 June 2012, Botev Plovdiv signed Kostov on a season-long loan deal,[1] with the option of making the move permanent.

Kostov earned his first cap for Bulgaria on 16 November 2018, coming on as a late second half substitute for Simeon Slavchev in the 1–1 away draw with Cyprus in a UEFA Nations League match.