Senegal forward Mane, who joined the Bundesliga champions from Liverpool last month, opened the scoring with a penalty, while de Ligt, signed from Juventus earlier this week, struck a volley from a corner to score Bayern's fourth.
Bayern's Serge Gnabry (27), Thomas Muller (32), Marcel Sabitzer (28) and Joshua Zirkzee (21) also found the net, while Skage Simonsen (24) and Theodore Ku-DiPietro's (20) goals gave DC United's fans something to cheer about.
Bayern next face Premier League club Manchester City in the United States, before flying back to Germany to take on RB Leipzig in the German Super Cup on July 30. DC United, who are bottom of MLS's Eastern Conference table, next play Montreal.