Both netted a goal each, while Rodrigo and Brahim Diaz also found the net in solid attacking performances as they secured a 4–1 win.
Modric, 38, finished with a wonderful cross to set up 20-year-old La Liga top scorer Bellingham, who fired a header past the goalkeeper for a 1-0 lead.
Los Blancos added a second chance shortly before half-time when Rodrigo headed home from close range after a scramble near the goalmouth.
Villarreal got an own goal early in the second half, with José Morales sprinting past the defense and past Andrey Lunin.
But it was a comfortable night for Madrid. Diaz scored the third after a winding run, before Modric got his deserved goal.
A neat finish into the bottom corner to turn the win into a defeat. It won't be easy, but Los Blancos got the job done
And are top of the table on Sunday night. Morales got a hand on the goal, but it's hard to say he should have saved it. Otherwise there is nothing to do.
Sometimes good, sometimes shaky. Always ready for aerial duels and comfortable on the ball, but got his positioning wrong on Villarreal's goal.