Lingard impressed on last summer's tour of South Africa but has still to make a first-team breakthrough and spent a short period on loan at Leicester last season.
"Jesse played well tonight," said Moyes.
"I was hoping he would get a hat-trick. For a young boy to get that at Manchester United is a big thing.
"He set up Robin for his goal with a nicely weighted pass, he worked really hard and showed a lot of maturity. It is good."