The in-form winger's goal-bound effort was deflected past Ben Foster by Baggies defender Ahmed Hegazi to double United’s advantage after 35 minutes.
Romelu Lukaku had earlier opened the scoring, while Gareth Barry set up a tense finale by prodding home from close range with 13 minutes remaining.
Lingard has been in fine form in recent weeks and if the goal is not taken away from him it will mean he has scored four times in his last six appearances.
"It was on target so I’m claiming the goal," he told Sky Sports.
"The first half was very comfortable and if we had added another goal it would have killed the game.
"We controlled the first half and thought we could carry that into the second half, but we had to drop a bit deeper. A win is a win, though."