Virgil van Dijk’s header put Jürgen Klopp’s title-chasers ahead at St. James’ Park, but Christian Atsu slotted home to level the scores soon after.
Mo Salah’s volley put the Reds back in front before the break, but Salomón Rondón produced a volley of his own to equalise once more in the 54th minute.
But substitute Origi won it for the visitors, glancing home fellow sub Xherdan Shaqiri’s free kick with five minutes left to keep them in the hunt for a first Premier League title.
Liverpool began with intent, with two early openings falling for Salah. The Egyptian winger snatched at his shot when Andy Robertson’s cross dropped kindly for him, before seeing another effort blocked by Paul Dummett when Sadio Mane’s centre picked him out at the far post.
And from the resulting corner, Klopp’s men seized the advantage. Trent Alexander-Arnold’s delivery was met by van Dijk, whose thumping header beat Martin Dúbravka.
But with 20 minutes gone, the Magpies levelled the scores. Former Liverpool man Javier Manquillo’s deep cross found Matt Ritchie at the back post, who in turn cut the ball back for Rondón. The frontman’s first-time strike was handled on the line by Alexander-Arnold but referee Andre Marriner didn’t stop play and Atsu followed up, tucking the equaliser past Alisson.
The goal heralded a spell of pressure from Newcastle, buoyed by a sell-out crowd of over 52,000 at St. James’. Ayoze Pérez forced his way into the box and produced a fine improvised shot which came back off the crossbar just before, with the visitors on the ropes, Ki Sung-yueng tested Alisson with a powerful drive.
The Reds continued to threaten on the counter attack, though, and retook the lead before the half hour. Alexander-Arnold’s cross found Salah, who guided his side’s second into the bottom left-hand corner past Dúbravka.
The Slovakian goalkeeper then denied Mane with a block when he went one-on-one, but United rallied after the restart. Rondón tested Alisson with a low drive as the hosts sought to build some momentum, though they could easily have gone two down when Daniel Sturridge blazed over after a flowing move from the Reds.
And that miss proved significant as Sturridge’s team conceded soon after. The Magpies hit back when Atsu’s run and cross earning a corner, which was only cleared as far as Manquillo. The full back nodded it back into the area and Rondón struck it first time with his unfavoured left foot. Alisson didn’t move as the ball flashed past him and nestled into the bottom corner.
Liverpool lost Salah to injury with just under 20 minutes left but, with Origi on in his place, kept pushing, and eventually they found a winner with five minutes remaining. Ritchie was penalised for a challenge on Fabinho and Shaqiri swung in the free kick, finding Origi, who glanced it past Dúbravka to snatch all three points and condemn Newcastle to defeat in their last outing at St. James' in 2018/19.