The Reds travelled to Yorkshire having suffered back-to-back defeats to Swansea City and West Bromwich Albion, but quickly took control of matters at the John Smith's Stadium.
Emre Can's 26th-minute drive put the visitors ahead and Roberto Firmino doubled their advantage with an intelligent finish on the stroke of half-time.
Mohamed Salah's cool penalty subsequently sealed the result in the second period - and left the captain delighted with the efforts of his colleagues.
"It was important for us after the last two results and performances that, obviously, we weren't happy with," Henderson told BT Sport.