Rashford broke the deadlock against West Ham in the 54th minute after a superb run and curling shot into the top corner.
Marouane Fellaini prodded in a second and United held on to book a Wembley date with Everton despite James Tomkins pulling a goal back with 11 minutes remaining.
Rashford has now grabbed six goals since he burst on to the scene in February, and the 18-year-old's latest may once again silence some of the calls for his manager to be sacked following an otherwise underwhelming season at Old Trafford.
Van Gaal said after the 2-1 win: "It was a great goal. I was behind it on the bench and saw the gap in the corner and shouted 'shoot', but to do it is much more difficult.
"A great goal and the dribble, also. He has that quality and he can score a lot of goals.
"He has no nerves, he's very focused on his work. I admire when you are so young and with so much attention now. He's scoring important goals.
"He can cope with that attention and focus on the next match, and when you have criticism he can cope also."
Source: PA