Lingard scored with a curling effort early in the second half before Mata secured the three points with a late penalty.
Lingard has enjoyed a run in the first-team in recent weeks and his performances have been encouraging.
Mata was full of praise for his teammate following the game.
“We have to make a positive assessment of the game against West Brom, a squad with former team-mates that made things complicated for us,” Mata wrote in his weekly blog.
“Lingard’s goal showed our way to the victory and I was lucky to close the score later on. It was his first goal with the first-team and here I congratulate him again. So, as I said, we face the international break in good spirits, feeling that we are working well and convinced that our game will get better.”
Lingard is going from strength to strength at United and Louis van Gaal deserves credit for placing his faith in the midfielder. It is fantastic to see an academy graduate and lifelong fan achieve his dream of not only playing, but scoring at Old Trafford.