Both Manchester clubs earned first-leg wins in the last 32 of the Europa League, but Stoke City were unable to make it a clean sweep for the English clubs.
United ran out 2-0 winners at Ajax, while City came from behind to earn a 2-1 victory at Porto.
However, Stoke have it all to do in the second leg after they lost 1-0 to Valencia at the Britannia Stadium.
Despite Ajax's defeat, it was an otherwise good night for the Dutch sides as AZ Alkmaar beat Anderlecht 1-0, PSV defeated Trabzonspor in Turkey 2-1, and FC Twente won 1-0 at Steaua Bucharest.
Falcao netted twice as Atletico Madrid won 3-1 at Lazio, but their Spanish counterparts fared less well as Athletic Bilbao were beaten 2-1 by Lokomotiv Moscow.
Andre Santos's late strike salvaged a 2-2 draw for Sporting Lisbon at Legia Warsaw, and the quickest goal of the night came in Austria as Taison scored in the first minute to set Metalist Kharkiv on their way to a convincing 4-0 win against Salzburg.
Klaas-Jan Huntelaar netted in the second half to give Schalke a 1-1 draw at Viktoria Plzen, while their fellow Germans Hannover claimed a 2-1 victory at home to Club Brugge.
