Inter were frustrated by more than an hour by their Bulgarian opponents until Eriksen fired a low shot into the net from just outside the penalty area in the 71st minute.
Romelu Lukaku sealed the win with a stoppage-time penalty, the Belgian striker's 22nd goal of the season, after Anicet Andrianantenaina was judged to have handled following a VAR review.
United were quickly in trouble in Belgium when Emmanuel Dennis lobbed the ball over Sergio Romero to give Brugge a 15th- minute lead, but Anthony Martial levelled in the 36th minute when he raced through to place a shot past Simon Mignolet.
United, with new midfield signing Bruno Fernandes on the bench, struggled to create many chances, although conditions were difficult with heavy rain and a strong wind.
Brazilian pair Deyverson and Kenedy scored in each half for Getafe against Ajax. Deyverson finished off a well-worked free kick to celebrate his European debut for the La Liga club with a goal after 38 minutes and Kenedy broke clear to add a second in the last minute.
Rangers came back from two goals down to beat Sporting Braga thanks to a brace by Ianis Hagi with Joe Aribo providing a third goal.
Wolves put four goals past a toothless Espanyol courtesy of a hat-trick by Diogo Jota, and an additional goal by Ruben Neves.
Meanwhile Arsenal triumphed over Olympiakos with a solitary goal from Alexander Lacazette.
In other matches, Daichi Kamada scored a hat-trick to help Eintracht Frankfurt to a 4-1 win over coach Adi Huetter's former club RB Salzburg. Viktor Kovalenko scored the winner as Shakhtar Donetsk beat Benfica 2-1 and Sporting defeated Istanbul Basaksehir 3-1. Youssef En-Nesyri equalised as Sevilla rescued a 1-1 draw at Cluj after Ciprian Deac had given the Romanians the lead with a penalty.
Bayer Leverkusen go into the second leg 2-1 over Porto, Basel inflicted misery on Apoel Nicosia with three away goals to their nil, and Wolfsburg beat Malmo 2-1. Roma took a 1-0 victory over Gent, and AZ Alkmaar drew 1-1 with LASK.