Liverpool had been pushed all the way by Championship side Bolton, who had taken them to a replay and with 10 men, were 1-0 up until Raheem Sterling's 86th minute equaliser.
Coutinho's winner saw rapturous scenes in the away end, and was the perfect note on which to cap a week in which the Brazilian signed a contract extension taking him up until 2020.
When the news broke on Monday that Coutinho had agreed his new deal, former defender Jamie Carragher said on Twitter that he needed to score more goals, if there was an area in which he needed to add to his game.
Last night he answered him, choosing his timing impeccably to hit the winner to continue his club's cup run.
The 22-year-old has now scored three goals this season, his strike adding to two he has netted in the Premier League.
Carragher was not the only ex-Red to praise Coutinho via Twitter, with former defender and current Brondby star Daniel Agger sending his old teammate a message.
Great win tonight and great winner by @Phil_Coutinho. Congrats on your new contract mate. Fully deserved