Fernandes netted again after half-time with a fine volley as United climbed above Wolves on goal difference to take fifth place in the Premier League.
The Portugal midfielder's role in revitalising United cannot be understated.
Brighton had taken four points from two games since the restart, easing their relegation fears, but this defeat means they aren't completely safe yet.
Solskjaer this week warned United's strikers they must improve if they want to stay in the team.
Cutting in from the right, Greenwood froze Lewis Dunk with a nimble step-over and drilled a low shot past Brighton keeper Mat Ryan at his near post.
There was frustration for Brighton as they claimed Shaw was offside and the ball had been taken out of play in the build-up to the goal.
Nemanja Matic's cross-field pass sent Greenwood sprinting away down the left and the teenager unfurled a perfect cross for Fernandes to volley past Ryan from 12 yards.