After opening the scoring from the spot after 20 minutes following a Leroy Fer foul on Adnan Januzaj, the 25-year-old reacted quickly to a Mark Bunn parry to double the hosts’ advantage with a header early in the second half.
Phil Jones made sure of the victory with a late volley, before Fabio prodded home a fourth in stoppage time in a game marred by a serious-looking head injury to Norwich's Robert Snodgrass.
The victory is United’s first over Norwich in the League Cup, and Hernandez has now scored in each of his last three appearances in the competition.
Wilfried Zaha was given a first start since August’s Community Shield win over Wigan Athletic, while Nemanja Vidic and Rio Ferdinand were also among those to come in.
Norwich were similarly unrecognisable from the weekend, with Fer, Bassong and Snodgrass the only players to line up at Old Trafford who started Saturday’s goalless draw with Cardiff City.
At the other end, Hernandez twice went close to giving United the lead in quick succession, but it wasn’t long before the Mexican broke the deadlock.
Norwich’s Fer, who has been under the spotlight since a display of unsporting behaviour in the Premier League clash with Cardiff, attracted more unwanted attention in the 19th minute as he left a lazy leg in the path of Januzaj inside the box to concede a penalty.
Hernandez stepped up and duly dispatched the spot-kick into the bottom left-hand corner of Mark Bunn’s net, sending the goalkeeper the wrong way to put United ahead.
