The Merseysiders defeated County 4-2 in the Capital One Cup second-round tie at Anfield.
And they required extra time to do it, with the score 2-2 after 90 minutes thanks to two second-half goals from the Sky Bet League One outfit.
Daniel Sturridge and Henderson netted in the additional period as Liverpool eventually managed to emerge triumphant from a contest in which they had initially looked set to rout their opponents.
Regardless of how it was achieved, though, the result was another win that extends the 100 per cent record of Brendan Rodgers' team this term to three matches following the 1-0 Barclays Premier League victories against Stoke and Aston Villa.
And Henderson sees it as crucial the run has been maintained ahead of Sunday's home league clash with Manchester United.
"It was a very important win to keep that momentum going," Henderson told www.liverpoolfc.com.
"We've made a good start and another win takes us on to the game against Manchester United.
"We'll go into that game very confident. We'll recover well from Tuesday night and everybody will be looking forward to the game come Sunday."
A fine solo effort from Raheem Sterling put Liverpool 1-0 up in the fourth minute and Sturridge doubled the advantage in the 29th after collecting the ball from a delightful Steven Gerrard pass.
Daniel Agger and Gerrard each hit the post in the opening 45 minutes as well and it seemed only a question of how many the Reds would win by.
But County rallied impressively after the break, with Yoann Arquin scoring a 62nd-minute header and then, after Kolo Toure had hit the post at the other end, substitute Adam Coombes slotting in an equaliser with six minutes of normal time remaining.
A groin injury to Toure saw Liverpool reduced to 10 men in extra time and the visitors then had penalty appeals rejected when Enda Stevens went down in the box under the attentions of Sterling.
But moments later, Sturridge's shot made it 3-2 on the stroke of extra-time half-time, and substitute Henderson then wrapped up the scoring in the 110th minute by bursting forward and finishing coolly.
Henderson, 23, said: "It was a bit of a relief to see the ball hit the back of the net.
"I think at 4-2 we knew the game was probably over as there was not long left.
"It was nice to score. The most important thing was to get the win. We would have liked it to have been a lot more comfortable, but things like that happen in football.
"We've got to go on and learn from it and make sure that if we're in that position again, we see the game out a lot more comfortably."
County boss Chris Kiwomya said: "I thought when Liverpool went down to 10 men, that was our chance to keep the ball from them.
"They looked resigned, as if it might be one of those days.
"But I felt like we just rushed it a little bit to score.
"We really believed we were going to win it. But with the players Liverpool have got, I knew how difficult it was going to be."
Meanwhile, Liverpool have confirmed they will pay tribute to their former manager Bill Shankly, one of the most famous figures in the club's history, during the build-up to Sunday's game.
Shankly was born 100 years ago on September 2.
There will be a minute's applause before kick-off and fans on the Kop will hold aloft cards to display a special mosaic.