The Biancocelesti looked set to cruise through to their first knockout tie in the tournament for 20 years when Joaquin Correa and Ciro Immobile scored either side of a Ruud Vormer strike and the away side had Eduard Sobol sent off before half time.
But the hosts, who simply needed to avoid defeat to progress, risked a spectacular collapse in the second half when Hans Vanaken headed the Belgians level as they pushed for a remarkable comeback.
Simone Inzaghi’s side ultimately held on for a point that secured them second place in Group F behind Borussia Dortmund, keeping their unbeaten run in the competition intact with four draws and two wins.
The hosts got off to a dream start when a clever Correa dummy sent Luis Alberto clean through on goal, and the Argentine striker was on hand to tap in a rebound after the Spaniard’s shot was parried by Simon Mignolet.
But Brugge responded almost immediately when Pepe Reina spilled a powerful shot and Vormer pounced on the loose ball to equalise from close range.
An entertaining encounter swung in the capital club’s favour again when Immobile was brought down in the box and stepped up to convert the resulting penalty, making it nine consecutive matches in all competitions that he has found the net for Lazio.
Brugge were lucky to still have 11 men on the pitch when Sobol, already on a booking, escaped a second yellow card after scything down Manuel Lazzari, but the left-back didn’t learn his lesson and incredibly hacked down the Aquile wing-back again just minutes later to earn a deserved expulsion.
Correa shot narrowly wide early in the second half and Immobile fired over from a promising position, but the visitors continued to press and were rewarded when Vanaken headed in from close range with 15 minutes remaining to set up a tense finale.
Brugge piled forward in search of a late winner and were inches away from achieving their goal in stoppage goal when Charles De Ketelaere crashed a shot off the underside of the cross bar, leaving the hosts relieved when the full-time whistle eventually blew.