The Spaniard kept out Leighton Baines' first-half penalty at Old Trafford on Sunday before producing a string of stunning saves in the dying moments as United held on to secure a second successive victory for the first time under Van Gaal.
Radamel Falcao scored the all-important goal, his 62nd-minute strike coming after Steven Naismith had cancelled out Angel Di Maria's opener.
But it was De Gea drawing plaudits from Van Gaal, who told BT Sport: "When you save a penalty and make three magnificent saves in the dying minutes, you are great.
"We won the game because of that."
The performance of Di Maria was impressive, too, with the Argentine continuing his stunning form since joining from Real Madrid in August.
United boss Van Gaal added in his post-match media conference: "When you set up and score goals, what more can you ask?
"When you do that every week, and he does, we have to be very pleased."
Van Gaal knows there is more to come from his players.
He said: "I have told the players, we are not playing well but we are fourth in the table. What is coming when we play well?"
The Dutchman also confirmed that Luke Shaw is unlikely to add to his on-going injury problems, suggesting the left-back - withdrawn after 70 minutes - was suffering from a "dead knee".
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