After last weekâ€™s 6-1 humiliation at home to Manchester City this result may not totally erase the memory but at least United have kept in touch with City at the top of the Premier League.
Everton started the game brightly but gradually the visitorâ€™s gained control and took the lead on 19 minutes as Patrice Evra crossed from the left giving Hernandez the simplest of chances from close range.
United really should have made their superiority count but as half-time approached it was Everton who finished the stronger, culminating in a Leighton Baines free kick hitting the crossbar with David de Gea a spectator.
The hosts took the game to United after the break but only in the closing stages did they look like finding an equaliser. In fact the Reds should have increased their lead but failed to make the most of some promising breakaways.
In a frantic last few minutes Everton had a couple of strong appeals for penalties turned down by the officials, particularly when Evra barged over substitute Magaye Gueye .
In the end United were grateful to their defence for this result with Nemanja Vidic and Jonny Evans outstanding.
Referee: Mark Halsey
Venue: Goodison Park
Man Utd scorers: Hernandez 19
TRIBAL ASKS: Why didnâ€™t Everton make more use of Fellainiâ€™s height. United looked uncomfortable when the ball was pumped up to the Belgian.
Yellow cards: Rodwell (EVE), Coleman (EVE), Fellaini (EVE)