Jude Bellingham scored to put Dortmund on course for an upset win before City hit back through a penalty by Riyad Mahrez and Foden's goal.
A 0-0 draw at Anfield in the quarterfinals on Wednesday protected a 3-1 advantage from the first leg for Madrid.
FC Goa produced a commendable performance to keep the side coached by the former Paris Saint-Germain manager at bay for the full duration of the match.
Chelsea qualified for the semifinals for the first time since 2014 despite a 1-0 loss to the Portuguese champions on Tuesday.
PSG stands one step away from the second final of its 51-year history and remains on course to win it for the first time.
City is still going for an unprecedented quadruple of major trophies this season, having reached the final of the English League Cup, the semifinals of the FA Cup and taken an 11-point lead in the Premier League.
The defending champion needs to make up a one-goal deficit in the second leg to avoid going out. Bayern lost the first leg 3-2 in Munich last Wednesday – Flick’s first defeat in the competition since he took over in November 2019.
Bayern lost the home leg 3-2 last week, and there have been only been five previous occasions in the elite event that a team has rebounded from such a defeat in the away leg
FC Goa will open their campaign at the continental club competition on April 14 against Qatar's Al-Rayyan.
ISL champions FC Goa will become the first club from the country to play in the continental club competition on April 14 when they take on Qatar's Al-Rayyan.
Bayern struggled to break through Union's stubborn defense until the 18-year-old Jamal Musiala finally made the breakthrough in the 68th minute.
UEFA’s chief refereeing officer Roberto Rosetti wrote to refereeing teams after the incident in the tunnel in Manchester on Tuesday night was caught on camera as the players left the field following Dortmund's 2-1 loss.
All of the team's group stage matches in the Champions League will be played in Goa. FC Goa face Qatar's Al-Rayyan in their first match on April 14.
Mason Mount and Ben Chilwell scored their first Champions League goals to give Chelsea a great chance of making it to the semifinals for the first time in seven years.
Bayern had 31 efforts at goal but missed Robert Lewandowski's accuracy, as PSG beat the German side 3-2 with only four shots on target altogether.
Bayern Munich vs PSG UEFA Champions League 2020-21 Live Streaming: Find full details on when and where to watch BAY vs PSG Live Online on SonyLIV and TV Telecast on Sony Ten Network.
Dortmund midfielder Jude Bellingham had his shot on target disallowed after the referee controversially cautioned him for fouling City goalkeeper Ederson just outside the box in the Champions League.
The Brazilian forward netted his first double for the club on Tuesday, leading them to a 3-1 over Liverpool in the first leg of the Champions League quarterfinals.
Foden netted City's 90th-minute goal to clinch a 2-1 victory over Haaland's Borussia Dortmund in the first leg of their Champions League quarterfinal.
After eliminating Juventus in the last 16, Porto hosts the first leg against Chelsea in a match that will be played in Seville, Spain, because of travel restrictions related to the coronavirus pandemic.
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