With the score goalless in the 35th minute, an accurate long pass over the home defence from Henderson found Oxlade-Chamberlain in behind and the latter poked a finish past the goalkeeper to break the deadlock.
The captain had felt there was an opportunity for his fellow midfielder to take advantage of direct deliveries in the game and his message was heard to important effect.
“He was probably moaning at me for the 20 minutes before that for not making enough of those runs, so I’m glad we managed to get that one right!” Oxlade-Chamberlain told Liverpoolfc.com.
“As he turned, I saw his touch and I went and he looked up and saw me straight away, and the pass was perfect. Luckily enough I could get my toe on it and finish it off, so I say thank you!”
Liverpool were on top for much of the contest at Vitality Stadium and clinched three points through further goals from Naby Keita and Mohamed Salah either side of half-time.
The result moved the Reds 11 points clear at the top of the Premier League, with Leicester City not in action until Sunday afternoon.
Jürgen Klopp’s team also registered their first clean sheet since September 28 in all competitions.
“It was a professional performance and a very solid performance. Overall, we are delighted with that,” said Henderson.
“Offensively, I thought we were very good, we kept the ball for large periods of the game and we defended really well as well, so overall we are really pleased.”
Oxlade-Chamberlain added: “Robbo and Millie were probably shouting at me for the last 30 minutes to just make sure we keep the clean sheet, and Robbo was shouting at me to make sure we kept it tight and be professional and not getting carried away going forward all the time.
“So, like Hendo said, it was really professional from start to finish really and I think it was probably the main thing we needed to improve on. In weeks gone by, we have gone 2-0 up and we just haven’t controlled the game well enough and we’ve made it difficult.
“Today, we learned from that and it was a really professional performance and some really top performances from all the boys.
“Naby came in and did really well, Hendo was brilliant in the middle as he always is, the boys at the back, and it was just a really good performance from everyone.”