Fernandes's first effort was saved by West Brom keeper Sam Johnstone but referee David Coote ordered the kick be re-taken after ruling the keeper had come off his line. The Portuguese midfielder made no mistake with the second attempt.
Winless West Brom's frustration was doubled by the fact that the penalty, awarded for a handball by Darnell Furlong, came eight minutes after they had a penalty award overturned after review.
Coote pointed to the spot after he ruled Fernandes made shin-to-shin contact with Conor Gallagher in the box but the referee reversed his decision after being sent to the pitchside monitor.
"Instead of us being one up, we are 1-0 down and it is hard to come back. We showed after that we didn't stop believing or playing. I'm very disappointed with the result and the decisions from the referee," said West Brom manager Slaven Bilic.
Substitute Callum Robinson went close to an equaliser for West Brom in the 65th minute with a superb curling shot that struck the bar.
United, who had struggled to break down Slaven Bilic's side until their goal, had chances to extend their lead but the outstanding Johnstone, a product of United's academy, made a series of good saves.
While the performance may have been lacking, United manager Ole Gunnar Solskjaer was pleased to get through a tricky game and come away with the points.
"It's nice after the international break that you get a win. We needed that win at home. We looked unsettled towards the end even though we should score one or two more to have a more relaxed finish," he said.
"Tight margins decide games but the mood is decided by the results. It's up to us to create momentum, we have the chance to continue the good start in the Champions League and Southampton away is a very difficult game as well. Hopefully, we get a few more back [from injury] and can kick on."