Manchester United recovered from their derby misery to beat Liverpool in the Capital One Cup third round, while holders Swansea exited after the first match in defence of their trophy.
Hernandez brought a sense of stability back to Manchester United after a turbulent week as his goal secured a 1-0 win in an absorbing tie with Liverpool.
Hernandez wriggled away from Jose Enrique to touch home Wayne Rooney's corner just after the half-time break.
On his return following a ten-match suspension, Luis Suarez came close to levelling when his vicious free-kick struck the bar with David De Gea beaten, but Liverpool -- who had named a strong side -- were unable to break through.
Arsenal are also through after they beat West Bromwich Albion at the Hawthorns on penalties following a 1-1 draw.
Thomas Eisfeld put the Gunners into the lead before Saido Berahino levelled to force extra-time. After a tense penalty shootout, Nacho Monreal scored the winning spot kick to secure the win.
Swansea's defence of the trophy ended at the first hurdle as they were knocked out courtesy of a resounding 3-1 defeat by Birmingham at St Andrew's.
It is just seven months and one day since Michael Laudrup's side lifted the first major honour in their 101-year history with a thumping 5-0 victory over Bradford at Wembley.
But the holders were brought crashing back down to earth by another side who also share fond recent memories of the competition -- 2011 winners Birmingham.
Papiss Cisse's first goal since April helped to ease Newcastle into the fourth round at the expense of Leeds with a 2-0 win.
Cisse's drought finally ended 31 minutes into a pulsating encounter when he powered a header past goalkeeper Paddy Kenny to end a run stretching back to the 1-1 Europa League draw with Benfica on April 11.
But the tie remained in the balance until deep into the second half when strike-partner Yoan Gouffran blasted home to wrap up a 2-0 win over the Championship side.
Stephen Ireland marked his first Stoke start with a goal as the Potters beat Tranmere Rovers 2-0.
Former England striker Peter Crouch added a last-gasp second as Mark Hughes' side saw off the League One side at Prenton Park.
Information from the Press Association was used in this report.