A much-changed United had the better of the early openings and deservedly took the lead in 21st minute as Brazilian forward Antony (22) curled a stunning strike into far corner.
Antony's fellow countryman Fred (29) then curled a sensational effort towards goal from a free kick, but saw his rasping shot come out off the inside of the post.
United had further chances to add a game-clinching second against Charlton before Rashford stepped off the bench to fire two late goals to put the seal on an eighth victory in a row in all competitions for the home side.
"I have told you many times, when he puts himself in the position, in one on ones in the box, he will score," coach Erik ten Hag said. "That is what he is doing at the moment. If he keeps the focus and keeps doing what he is doing, he will score more.
"First half I was happy, but I was less happy with not being clinical in front of goal. We created a lot of chances. We should have scored more.
"Sometimes we need that extra pass. We had to fight right until the end.
"But we are scoring goals from the back, from set plays too, so I think we are progressing."
