Senegalese international Mane, who joined Bayern from Liverpool last month, opened his account for the Bundesliga champions from the penalty spot after five minutes.
Bayern doubled their lead in the 12th minute when Marcel Sabitzer's shot from outside the area wrong-footed D.C. United goalkeeper Jon Kempin. Serge Gnabry made it 3-0 just before half-time, tucking away a low cross from Mane in the 44th minute. De Ligt then marked his move from Italy's Juventus earlier this week with a goal on debut after coming on as a substitute at half-time.
Joshua Zirkzee added a tap-in after a patient build up from Bayern to make it 5-0 in the 51st minute before Skage Lehland's consolation effort for D.C. United three minutes later. Theodore Ku-Dipietro added a second for D.C. United three minutes from time before German veteran Thomas Mueller made it 6-2 deep into injury time.