Everton had produced an admirable performance and could have ended their infamous Anfield hoodoo had they taken one of their numerous first-half chances, but just as it looked as if they had done enough for a point, Liverpool snatched all three in stunning circumstances.
Trent Alexander-Arnold saw his long punt forward cleared as far as Virgil van Dijk, whose skewed long-range effort appeared to be heading for the top of the crossbar, only for Pickford to inexplicably palm it back into the air, the ball then bouncing off the woodwork and into the path of substitute Origi, who had the simple task of nodding into an empty net.
It means Liverpool – whose manager Jurgen Klopp sprinted onto the pitch to celebrate – stay within touching distance of champions Manchester City, who they trail by just two points, with the Reds continuing to look like the most likely challengers to Pep Guardiola's side.
Everton – winless at their rivals' ground since 1999 – had a gilt-edged chance to take the lead in the fourth minute when Yerry Mina, incorrectly not flagged for offside, somehow headed Lucas Digne's free-kick wide with the goal at his mercy.
Liverpool responded well to that scare and Sadio Mane lashed over from Mohamed Salah's clever ball. However, it was Everton who had the better of proceedings, and they will have been left wondering how they did not take the lead when Alisson produced heroics to preserve parity.
Theo Walcott headed Bernard's superb far-post cross back to Andre Gomes, whose point-blank header was magnificently kept out by Alisson's flying save. Gylfi Sigurdsson attempted to bundle home the rebound in the resulting goalmouth scramble but Joe Gomez cleared off the line in the nick of time.
Pickford denied Xherdan Shaqiri with his leg at the other end, but the Toffees spurned another glorious opportunity when Walcott lost control of the ball after rounding Alisson.
Liverpool were much improved after half-time and Salah curled wide before Mane again missed the target following good work from Roberto Firmino.
Mane's wayward shooting performance continued as he failed to trouble Pickford from the edge of the area, and the Reds' hopes of triumph looked to have gone when Origi clattered against the crossbar from two yards out and Liverpool saw appeals for handball against Sigurdsson waved away by referee Chris Kavanagh from the follow-up.
Yet that proved only a prelude to a bizarre ending as Origi, brought on in the 84th minute playing in his first Premier League game since the beginning of last season, took his second chance to write his name into Merseyside derby folklore, sparking scenes of wild celebration typified by Klopp's sprint to rejoice with Alisson.
What does it mean? Off-colour Reds keep pace at top
Liverpool had the greater share of possession, but their performance did not really merit all three points and the reaction of manager of Klopp showed just how important it is to avoid slip-ups when attempting to chase down a foe as formidable as City.
Origi gifted a fairytale finish
Origi's move from Lille to Liverpool has largely proven a disappointing one, the Belgium international spending most of last season on loan at Wolfsburg, but he will hope the gift provided to him by Pickford will spark a revival in his Anfield career.
Derby misery for Pickford
Pickford has consistently been an excellent performer for Everton and was superb for England at the World Cup, but his error in a game of such magnitude will take a long time to live down.
Key Opta Facts
- Liverpool have recorded five 90th-minute winners against Everton in the Premier League; more than against any other side in the competition.
- The Reds have kept 21 clean sheets against Everton in the Premier League; more than they have accumulated against any other side.
- Liverpool are unbeaten in each of their last 18 matches against Everton in all competitions (W9 D9) – the Reds' longest unbeaten run against their rivals.
- Jurgen Klopp's side have recorded 11 clean sheets in the Premier League so far in 2018 at Anfield; only in 2002 and 2006 have the Reds kept more (12).
- Liverpool have conceded just five goals in their first 14 Premier League games this season; only Chelsea in 2008-09 conceded fewer at this stage in a Premier League campaign (4 goals).
- Divock Origi has scored in all three of his home league appearances against Everton for Liverpool – scoring more goals against the Toffees than any other side in the competition.
Both sides have to contend with teams fighting at the wrong end of the table next up. Liverpool travel to Burnley while the visit of struggling Newcastle United to Goodison Park could prove the perfect tonic to any hangover Everton have from this game.