They will be joined in the knockout stages by Juventus, who won by the same score at Olympiacos with Juan Cuadrado and Federico Bernardeschi on the scoresheet.
The Premier League's representatives are flying high in the Champions League this season and all five look set to romp into the final 16.
United finished the group phase with a 2-1 victory over CSKA Moscow at Old Trafford while Chelsea drew 1-1 with Atletico Madrid.
Seeded group winners will be away in the round of 16 first legs on 13/14 and 20/21 February and at home in the return matches on 6/7 and 13/14 March.
Former Chelsea star Michael Essien believes the side's Premier League title ambition is far from over, despite now trailing leaders Manchester City by 11 points. Sevilla can win Group E with a win if Liverpool fails to defeat Spartak Moscow at home.
Germany's representation in the last 16 could come down to just one team, Bayern Munich, after disappointing campaigns from the Bundesliga's best Borussia Dortmund in particular.
Manchester City have already won group F ahead of their final game against Shakhtar Donetsk. If Porto finish level on points with Leipzig, the Portuguese side will qualify due to their better head-to-head record. Sevilla only need to draw with Maribor in Slovenia to qualify for the knockout stage, and would go through as group winners if they win and Liverpool slip up. Filling out the rest of the bracket and who takes four of the eight group victor spots is still in play.
Diego Perotti's second-half goal saw Roma beat Qarabag 1-0 to top Group C ahead of Chelsea, who were held to a 1-1 home draw by Atletico Madrid, who will play in the Europa League.
"We want to win and sing together", Di Francesco posted on social media.
After putting seven goals past Celtic two weeks ago in Group B, PSG and its impressive offensive armada of Neymar, Kylian Mbappe and Edinson Cavani will also try to improve what is already a tournament record of 24 goals in this season's group stage.
Chelsea won't challenge for the Premier League title this season given the distraction of the Champions League, Stan Collymore has claimed.
Shakhtar need a point to secure their progress to the round of 16.