Hans Vanaken equalised for the home team from the penalty spot before the break, and it was Brugge who created the better chances in the second period without reward.
Lazio were missing a number of their leading players following a COVID-19 scare in their camp with striker Ciro Immobile and midfielders Luis Alberto, Manuel Lazzari, Lucas Leiva and Djavan Anderson all staying in Rome.
Lazio and Brugge have four points at the top of the group after two rounds, with Borussia Dortmund on three and Russian side Zenit Saint Petersburg yet to break their duck.
Lazio looked the more likely to score in the early stages and were rewarded for their ambition after 14 minutes when Correa produced a neat piece of skill on the edge of the box to wrong-foot Brugge defender Simon Deli and curl the ball into the corner of the net.
But the home side grew as a force as the half wore on and Charles de Ketelaere should have had them level when he collected a pass six metres from goal but skewed his shot wide when it seemed easier to hit the target.
Brugge found their equaliser just before halftime though after Lazio defender Patric Gabarron wrapped his arms around Mats Rits at a corner.
Referee Anthony Taylor initially waved play on but was drawn to the pitch-side screen to review the decision and pointed to the spot for Vanaken to convert.
Emmanuel Dennis was denied by Lazio goalkeeper Pepe Reina from a tight angle, before the experienced gloveman saved superbly to keep out Rits's header and Eduard Sobol shot wide at the back post as Brugge finished strongly.