Swift advancement comes as a boost to Tuchel, who insists his future lies in Paris, but this was far from a vintage performance.
The Ligue 1 champions have four wins from four in the competition this season, while they are still to concede, yet both records would have been tarnished had Keylor Navas not saved Mbaye Diagne's penalty in a particularly poor second half.
PSG scored inside seven minutes en route to a 5-0 win in Belgium a fortnight earlier but laboured early on this time around until a fortuitous bounce fell Icardi's way midway through the first half.
The on-loan striker had been a peripheral figure to that point, yet he could hardly have missed as Colin Dagba's low cross deflected through Simon Deli's legs for a simple tap-in.
The hosts still were not entirely convincing and would have been pegged back on 50 minutes but for Navas' reactions.
The goalkeeper scrambled to keep out an Emmanuel Bonaventure Dennis effort that struck David Okereke and span towards goal, before bouncing to his feet to deny the latter again on the rebound.
Dagba struck the outside of the post as he sought to force in a strike from an improbable angle in a swift PSG riposte, but Tuchel's side stalled again and were once more grateful to Navas.
Thiago Silva was punished for a clumsy challenge on substitute Diagne, who took the spot-kick himself but sent a tame effort straight into the hands of the keeper.
What does it mean? PSG scrape through, Brugge still in it
It is job done for PSG, who are into the last 16. A draw might have been a fairer outcome, but they took their one big chance when it arrived. This game should still have buoyed Brugge, though, as they plot their own unlikely path to the next round. They will have to beat Real Madrid but have already caused a stir at the Santiago Bernabeu.
Icardi in top form
Icardi's issues at Inter have already been forgotten amid an oustanding start to life at PSG, with his tally swelling week by week. The forward's career Champions League record is similarly impressive, scoring eight times in his first 10 matches - one shy of a record held jointly by Sadio Mane, Simone Inzaghi and Harry Kane.
8 - Mauro Icardi 🇦🇷 has scored 8 goals in his first 10 games in the Champions League, only Sadio Mané, Simone Inzaghi & Harry Kane have done better in the history of the competition (9 each). Hurry. #PSGCLU pic.twitter.com/3FoN0sCOvm— OptaJean (@OptaJean) November 6, 2019
Kylian kept quiet
Mbappe scored a second-half hat-trick from the bench in the reverse fixture but, by his lofty standards, was extremely quiet in Paris. The World Cup winner toiled on the flank in the first period and then miscued in front of goal prior to Dagba hitting the woodwork following the restart.
PSG return to league action at Brest on Saturday, before going to Real Madrid later this month - where Brugge will hope for a favour from Tuchel's men. In the meantime, the Belgian club are away at Royal Antwerp this weekend, visiting Galatasaray for their next European task.