Barcelona, dropping their first points in four matches, had two-thirds of the possession and pressed hard for a winning goal to deafening opposition from fans at Karaiskakis Stadium.
PSG have won their four matches so far in Group B - scoring 17 goals while conceding none - and are three points clear of Bayern Munich.
An action-packed group stage set up for sure as Atletico Madrid need a must win if they are to qualify. Take a look at the Champions League group matches fixtures this week.
Edin Dzeko's double had briefly put Roma in front but 2012 Champions League winner Chelsea remains two points ahead of the Italian club at the top of the group.
Young Belgian goalkeeper misjudged Rashford's shot and couldn't stop his momentum after stepping back toward the goal to make the catch.
Messi managed the feat in 122 European matches, 21 fewer than Ronaldo needed to score his 100th European goal in April.
Dortmund, which reached the final in 2013, started well against a side that hadn't scored in its previous six games but then stagnated as APOEL organized.
Manchester City beat Napoli 2-1 in their Champions League Group F match on Tuesday, maintaining their 100 percent record after three games.
Tottenham proved tough to crack against the defending champions at Santiago Bernabeu Stadium and held on for the draw that kept both clubs at the top of Group H.
Alvaro Morata had added to his impressive start with Chelsea by scoring a second-half equalizer after Atletico had taken the lead before halftime with a penalty converted by Antoine Griezmann.
Mbappe, who was hired alongside Neymar this summer, did not score but tormented the Bayern defence throughout with his dribbling ability and frenetic pace. He was decisive in setting up Neymar's goal.
The ugly slog of a match was interrupted in the 90th minute when a fan invaded the pitch to approach Messi, before being escorted off.
United's second win in two Champions League games leaves it top of Group A.
The ace striker was criticized by many after a poor performance in a 1-0 home loss (Real Madrid) against Real Betis in the Spanish league.
Tottenham, which beat the German side 3-1 in their opener at Wembley Stadium, defeated APOEL with a Harry Kane hat trick, his sixth of the year.
Kevin De Bruyne and Raheem Sterling scored as Manchester City beat Shakhtar Donetsk to take the group's lead with six points.
Ronaldo, yet to score in the Spanish league where he sat out a five-game suspension for shoving a referee, took his tally in Europe's premier competition this season to four goals in two games as he sent Dortmund to its second straight defeat.
Liverpool dominated the attack but Firmino and substitute Daniel Sturridge missed good chances, while Mohamed Salah had a header saved deep into injury time.
The Spanish giants don't seem to miss their winger as it has been Lionel Messi who has been netting in goals consistently since the Brazilian's departure.
The Reds' attacking play was thrilling once again, but defensive uncertainty continues to plague the team.
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