Origi got a decisive touch to fellow substitute Xherdan Shaqiri's free-kick to lift Jurgen Klopp's side off the canvas and back two points ahead of Manchester City, who visit Leicester City on Monday before the season comes to an end next Sunday.
The Reds' dreams appeared to have slipped away after Salomon Rondon fired in Newcastle's second equaliser in the 54th minute, which preceded a concerning head injury that forced Mohamed Salah off on a stretcher.
Virgil van Dijk and star man Salah had earlier scored either side of Christian Atsu's close-range strike, but it was Origi who provided the match-winning moment in a see-sawing contest.
Defender Van Dijk lit the fuse on a rollicking match by punishing Newcastle's shambolic marking in the 13th minute.
Trent Alexander-Arnold delivered the corner for his fellow defender's free header and was fortunate to avoid sanction as the hosts issued a swift response.
Rondon's close-range shot bounced back off the right-back's arm and was swept in by Atsu in the 20th minute, with referee Andre Marriner leaving the goal-line handball unpunished.
His decision came into sharper focus moments after Ayoze Perez fired against the crossbar.
Liverpool ventured forward, Alexander-Arnold crossed from the right and Salah guided home a deft right-footed finish.
Daniel Sturridge squandered a good opportunity after the interval and Rondon soon gave him a lesson in finishing, rifling into the bottom-right corner after Javi Manquillo won a header on the edge of the area.
And, 72 hours on from the crushing Champions League loss to Barcelona, Liverpool's chastening week seemed set to end with the sight of Salah in anguish after a heavy collision with the onrushing Martin Dubravka.
But there was a final twist to come as Origi's attempted header flicked in off Jamaal Lascelles and returned the pressure back to champions City.
This TEAM.— Liverpool FC (@LFC) May 4, 2019
UP THE REDS! pic.twitter.com/15EbUPOrx7
What does it mean? Reds pass almighty test of character
Rafael Benitez pledged to do no favours for his former employers and that promise played out across an epic encounter that lasted for almost 100 minutes.
Liverpool dug deep into endless energy resolves and retrieved a result that ensures their battle with City will go right down to the wire. Whatever the outcome of their bid to win the league for the first time in 29 years, Liverpool can be immensely proud of their efforts.
Rondon runs defenders ragged
Van Dijk, the newly crowned PFA Players' Player of the Year, has been outstanding all season for Liverpool, but he has hardly encountered a challenge quite like that provided by Rondon on Tyneside. The imposing striker constantly asked questions of the away side's normally imperious defence, played a prominent part in the first equaliser, and then conjured a fine goal that almost earned the Magpies a hard-earned point.
Lascelles struggles at set-pieces
Illness kept Lascelles out of Newcastle's draw at Brighton and Hove Albion last time out and he might have wished he stayed in bed on Saturday. He lost Van Dijk for the opener and was unable to contain Origi for Liverpool's late winner.
Key Opta Facts
- Newcastle have conceded 98 Premier League goals against Liverpool, more than against any other side.
- Salah scored his 100th league goal in European top-flight football, with 56 of those coming in the Premier League (also 35 in Italian Serie A and 9 in Swiss Super League).
- Liverpool are the first team in Premier League history to have at least two defenders provide 10+ assists each in a single campaign (Trent Alexander-Arnold 11, Andy Robertson 11).
- Rondon has hit double figures for goals in a Premier League season for the first time ever.
Liverpool, trailing 3-0 after the first leg of their Champions League semi-final tie, will attempt to pull off an unlikely comeback at home to Barca on Tuesday, before Wolves visit Anfield on the final day of the Premier League season. Newcastle's last assignment of 2018-19 takes them to Fulham.