The Mexico striker was on hand to put United ahead mid-way through the opening 45 minutes.
Everton pressed for an equaliser after the interval but they were unable to break down the visitor’s defence, with Nemanja Vidic starring at centre-half.
The victory keeps United in second place in the table, three points behind leaders Manchester City.
The home side started well, looking to capitalise on a United team experiencing a crisis of confidence following last weekend’s heavy derby defeat by Manchester City.
Seamus Coleman tested David de Gea within the first twenty seconds – but the winger had his shot saved at the near post.
United responded immediately. Danny Welbeck, partnering HernÃ¡ndez up front with Wayne Rooney dropping into midfield, broke into the box and squared to Park Ji-Sung, who forced Tim Howard to produce a sharp save.
Rooney, returning to the ground where he started his career over seven years ago, endured a quiet afternoon and his only sight on goal came after 17 minutes when he prodded a shot harmlessly wide of Howard’s right post.
Unsurprisingly, it was HernÃ¡ndez who produced the vital goal to decide a tense game.
Tom Cleverley and Welbeck combined to release Patrice Evra down the left wing – and the French defender delivered an inch-perfect cross which HernÃ¡ndez clinically turned into the net inside the six-yard box to edge United ahead.
The home side responded and enjoyed a spell of sustained pressure before the break.
Leon Osman and Jack Rodwell both unleashed low shots which had De Gea scrambling, before Leighton Baines came closest for Everton five minutes before half-time.
Referee Mark Halsey penalised Darren Fletcher for a cynical foul on Marouane Fellaini and Baines sent the resulting free-kick over the static United wall and crashing onto the crossbar, much to the relief of United’s shot-stopper.
In the second half, Ferguson instructed his players to sit back and counter-attack, while Moyes’ side poured forward in search of an equaliser.
Coleman, who was a constant threat on the Everton right wing, pressured Jonny Evans into a dreadful clearance and Rodwell seized possession, unleashing a dipping effort which smacked De Gea in the face and deflected wide.
United had their own chance to seal victory shortly after, when hesitancy from Everton substitute Ross Barkley allowed Rooney to pinch the ball.
HernÃ¡ndez fired a cross-field past to Welbeck – but with the England international looking a certainty to score, former United keeper Howard punched Welbeck’s effort over the crossbar.
An injury to Cleverley forced Ferguson to introduce Nani – and the absence of the England midfielder’s calm presence at the heart of United’s midfield was evident as the visitors struggled to keep possession for the remaining 30 minutes.
Apostolos Vellios and Magaye Gueye came on as Everton desperately tried to break down the United rearguard – but the visitor’s defence stood firm, expertly marshalled by Vidic.
Everton had a penalty claim turned down in the dying moments when Halsey adjudged there to be minimal contact between Gueye and Evra in the United area, despite the left-back leaning into the Toffees forward and causing the substitute to slip.
And the defending champions held firm despite six minutes of stoppage time and continued their rehabilitation frollowing last Sunday’s drubbing at Old Trafford.
Everton: Tim Howard, Johnny Heitinga, Tony Hibbert, Phil Jagielka, Leighton Baines, Marouane Fellaini, Seamus Coleman, Diniyar Bilyaletdinov (Ross Barkley, 45), Leon Osman (Apostolos Vellios, 76), Jack Rodwell, Louis Saha (Magaye Gueye, 84).
Manchester United : David De Gea, Patrice Evra, Jonny Evans, Phil Jones, Nemanja Vidic, Tom Cleverley (Nani, 57), Park Ji-Sung, Darren Fletcher, Danny Welbeck (Antonio Valencia, 73), Wayne Rooney, Javier HernÃ¡ndez (Dimitar Berbatov, 67).
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