The Mexican tapped in after 19 minutes to get the champions back on track in the Premier League after last week's 6-1 thrashing by Manchester City.
Yet it was a far from convincing performance by United and Everton twice went close to equalising as Leighton Baines hit the bar and David de Gea saved brilliantly from Jack Rodwell.
Everton also had plenty of possession in the closing stages of each half but lacked the cutting edge to truly worry the visitors.
United boss Sir Alex Ferguson had given Jonny Evans a vote of confidence following his sending off against City by restoring him in defence after suspension.
Evans took his place alongside Nemanja Vidic, himself sent off on Champions League duty recently, with Rio Ferdinand left on the bench.
Otherwise United's emphasis was on attack with Hernandez, Danny Welbeck and former Everton prodigy Wayne Rooney all starting.
Everton had problems with experienced pair Phil Neville and Tim Cahill ruled out, in-form Royston Drenthe suspended and defender Sylvain Distin unexpectedly missing from the teamsheet.
That meant Phil Jagielka, who had been doubtful due to a hairline toe fracture, was pressed back into service.
Everton were the first side out of the blocks as Seamus Coleman burst down the right, cut inside Patrice Evra and fired a shot at David de Gea with just 15 seconds on the clock.
The visitors started brightly too with Welbeck jinking into the area and pulling back for Park Ji-sung at the near post, but the Korean's effort was blocked by former United keeper Tim Howard.
A chance appeared to open up outside the box for Rooney, whose reception from the Goodison crowd was not too bitter, but referee Mike Halsey got in the way and he stabbed wide.
United claimed the lead when an Evra cross found its way to Hernandez in front of goal.
Jagielka was unable to reach the ball from the left and Hernandez tapped in unmarked.
Welbeck almost sneaked in on goal when Jagielka headed back towards Howard after an awkward bounce but the American just beat the striker to the ball.
Everton responded as Leon Osman first won a free-kick off Vidic on the edge of the box after beating the Serbian with a nice piece of skill.
Another former United player, Louis Saha, shot into the wall and Osman forced De Gea to save when the ball was eventually worked back in. Moments later Rodwell seized possession but drove wide.
Everton maintained the pressure as Marouane Fellaini won another free-kick in a good position five minutes before the interval when felled by Darren Fletcher.
Baines, who missed a penalty in the Carling Cup in midweek, stepped up and curled a superb effort against the crossbar.
Saha had another couple of opportunities before the break but failed to trouble De Gea.
Some intricate one-touch passing from United put Welbeck through in the opening moments of the second half but the striker was unable to control the final ball.
Rodwell extended De Gea for the first time when he cut inside onto his left foot from the right but the Spaniard produced a fine save to his right.
United immediately countered as Tom Cleverley, making his first Premier League appearance in seven weeks after recovering from a foot injury, released Hernandez with a brilliant long pass.
Hernandez came inside but lacked options and slowed, allowing Everton to come clear.
That proved to be Cleverley's last major involvement as he limped off shortly afterwards to be replaced by Nani.
Hernandez then picked out a charging Welbeck with a crossfield pass but Howard reacted quickly to palm out his volley.
Everton pressed again with Saha twice having shots blocked in a goalmouth scramble before Rodwell blazed over. Coleman got an attempt on target but again failed to trouble De Gea.
The game went into six minutes of injury time, caused in part by an injury to an assistant referee which forced fourth official Phil Dowd into emergency action on the line.
Home fans wanted a penalty when Saha went down in the area but replays showed the Frenchman slipping and colliding with Evra.
After that United held firm. They may have beaten Aldershot in the Carling Cup on Tuesday but this victory, in spite of the performance, will do much more for their confidence as the shockwaves from Old Trafford last week continue to reverberate.