Opportunities were also hard to come by in the second period before substitute Toffees goalkeeper Joel Robles did well to parry Roberto Firmino‘s volley with 10 minutes remaining.
There was still a chance for Firmino to slot home a second for the Reds within the additional nine-and-a-half minutes added by referee Mike Dean but Seamus Coleman managed to clear brilliantly off the line.
The result lifts Liverpool up to second, six points behind leaders Chelsea, and captain Henderson was delighted to pick up the win.
“It’s a great feeling to come here on derby day and win, there’s no better place to win away from home,” he told Sky Sports.
“I thought the boys were brilliant, especially at the end of the first half.
“In the second half I thought we dominated and could have scored a couple more but, in the end, we’re delighted with the 1-0 win.”
The England midfielder added: “It gives us great confidence no matter where we are in the league.
“We have got to keep focussed on ourselves on each game every week, that’s all we can do.”
Ross Barkley’s second-half lunge on Henderson saw the Everton midfielder booked by referee Mike Dean, and the Liverpool skipper played down the incident.
“It was pretty late, but I know Ross well, he’s a good lad, I’m good friends with him,” added Henderson.
“I think he just mistimed the tackle, Obviously after the game he apologised, it was a little bit late.
“Thankfully I’m all right. It was just mistimed, you’re going to get them in derby games.”
Everton boss Ronald Koeman accepts Barkley was a little fortunate not to have been sent off for the high challenge on Henderson.
The Dutchman, though, questioned whether Coleman deserved a booking for his actions in the subsequent scuffle between the two sets of players.
Koeman said: “Why [Mike Dean] gave Coleman a yellow and not Lovren, I don’t know. Everybody was reacting and it was started by Lovren and he already had a yellow.
“Maybe [Barkley] was lucky because maybe it was a red card, but after that happened, the reaction was started by Lovren, and not by the Everton players.”
Koeman added: “It was a very good team performance, but we made it very difficult. We had it more difficult in the second half.
“We did everything that we could tonight, we didn’t keep the ball in the second half as well as we did in the first half but the team didn’t deserve to lose. The fight in the team was still good.”
He said: “It was quite intense, and I’m very, very happy after the game.
“You saw the reaction of our fans, so obviously they were happy and that’s the best you can do on a night like this.
“If you only win games on your brilliant days you don’t win a lot of games. Today was a real fight, a real battle, we were ready for it and we’re happy.”