Brugge had already secured a place in the last 16 as the first Belgian club to reach the knockout stage since Gent in 2015-16.
Combined with Porto's 3-0 win over Atlético Madrid in the other game in Group B, the draw with Leverkusen meant that Brugge missed out on becoming the first team from Belgium to win a Champions League group since Anderlecht 22 years ago. Leverkusen placed third and heads to the Europa League ahead of Atlético.
The game started at a slow pace before gradually gathering intensity. Brugge's Kamal Sowah forced a good save from goalkeeper Lukas Hradecky in the 39th minute before Leverkusen's Jeremie Frimpong hit the side netting in first-half stoppage time.
Both teams came close to taking the lead early in the second half, with Brugge's Canadian winger Tajon Buchanan blasting a shot against the crossbar in the opening seconds of the half. Former Liverpool goalkeeper Simon Mignolet stopped Brugge from falling behind when he pushed a dangerous Patrik Schick header over the bar at a corner.
The draw leaves new Leverkusen coach Xabi Alonso winless in six games following a victory over Schalke in his first game in charge on Oct. 8 as his team has slipped to third from last in the Bundesliga. It's the first top-division coaching job for the former midfielder, a two-time Champions League winner with Liverpool and Real Madrid.