English midfielder Bellingham, who joined Madrid from Borussia Dortmund in a $114 million deal in June, scored his first goal after only six minutes.
With a perfectly weighted ball that sent Bellingham bearing down on goal, Madrid defender Antonio Rudiger took the United defense off guard.
The 20-year-old used one touch to gain control before lifting an exquisite chip over United goalkeeper Andre Onana to give Madrid a deserved lead.
Vinicius Jr., a Brazilian international, might have doubled Madrid’s advantage immediately after, but he scuffed his effort from eight yards out, letting United off the hook.
Meanwhile, United nearly equalized after 36 minutes, but Marcus Rashford was unable to reach the target from a tight angle.
With Madrid in command, United’s rage erupted shortly before halftime when Lisandro Martinez clattered into Bellingham with a violent tackle. Martinez was booked for the challenge when Bellingham reacted furiously.
After a flurry of substitutions at halftime, United looked brighter after the break, but Madrid generated more chances, with Militao almost making it 2-0 on 69 minutes only to have his shot pushed off the line.
In the 89th minute, Lucas Vazquez crossed for veteran forward Joselu to light up the NRG Stadium with a magnificent overhead ƙicƙ, putting Madrid up 2-0.