Liverpool 2 Sunderland 0: Black Cats go bottom again after Anfield defeat
The Black Cats produced a spirited display for the first half, well organised and defending well but relentless Liverpool ultimately proved too strong.
Origi broke the deadlock from a tight angle in the 75th minute before Milner secured the points late on from the penalty spot.
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Hide AdIt means Sunderland, who had gone into the game at Anfield on the back of wins over Bournemouth and Hull City, drop back to the bottom of the Premier League.
David Moyes had made two changes, with Steven Pienaar and John O'Shea returning to the side.
Pienaar replaced Paddy McNair who is facing a long spell on the sidelines with a knee injury, while O'Shea replaced the suspended Papy Djilobodji at centre-half.
Jason Denayer was deployed in the holding midfield role again, with the Belgian loanee given strict instructions to man mark Liverpool dangerman Philippe Coutinho.
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Hide AdSunderland lined up in a 4-1-4-1 formation with Victor Anichebe wide left and Duncan Watmore wide right when Sunderland didn't have possession.
Jordan Pickford was twice called into action to make low saves in the opening 15 minutes; Roberto Firmino shooting on the turn before Georginio Wijnaldum tried his luck from a similar
distance.
Sunderland looked a threat on the counter-attack, with Loris Karius called upon in the 17th minute to deny Pienaar's effort from six-yards out.
The midfielder had latched onto a long Billy Jones pass upfield but Karius made a vital save, pushing the ball out for a corner.
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Hide AdLiverpool were dominating the possession but Sunderland looked solid at the back, with Firmino firing a sweetly-hit shot wide from 25-yards before Wijnaldum dragged an effort well wide.
Sunderland had a penalty appeal turned down 29 minutes in, Pickford's missile-seeking clearance picked up by Defoe, who went down under a challenge by Joel Matip.
Replays showed there was little in it though, with referee Anthony Taylore making the right decision not to award a spot kick.
Liverpool were then dealt a blow, with Coutinho carried off the pitch on a stretcher after coming off worse from a block tackle with Ndong.
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Hide AdThe best chance of the half came in the 37th minute, Dejan Lovren sending a header wide of the right-hand post from a deep Jordan Henderson free-kick.
It should have been the opener.
Emre Can then had two attempts with his head, one he got horribly wrong, the ball going high and wide from a Henderson corner. The second he nodded wide of the post.
Lovren then tried his luck from 30-yards in the 45th minute, his fierce effort sailing just wide of the left-hand post, with Pickford at full stretch.
Jurgen Klopp's Liverpool side dominated possession, with 80 per cent of the ball compared to Sunderland's 20 per cent.
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Hide AdBut well-organised Sunderland, who had defended with real determination, held firm and went in level at the break.
Half-time: Liverpool 0 Sunderland 0
Liverpool started the second half as they had ended the first, with Sunderland on the back foot.
Sadio Mane's weak effort at goal a let-off for the Black Cats in the opening minutes of the second half.
James Milner was inches away from opening the scoring in the 52nd minute, but under pressure from Watmore at the back post failed to connect with Wijnaldum's volley.
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Hide AdSunderland were camped in their own half, with Liverpool pressing them back. Firmino's tricky footwork created an opening for himself but Pickford got down well to save.
It was a fine stop from the England Under-21 keeper. Kone booked minutes later for kicking the ball away after conceding a free-kick.
The home support was becoming increasingly frustrated, Klopp doing his best to rally them from the confines of his technical area.
Can shot wide 65 minutes in, with Sunderland doggedly digging in at a bitterly cold Anfield.
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Hide AdWatmore, Pienaar and Anichebe were all involved in a goalmouth scramble as Sunderland enjoyed a rare attack but Liverpool cleared the danger. Watmore's touch heavy.
Liverpool then flexed their muscles again, Firmino flashing a pass across the face of goal before Henderson curled a free-kick over Pickford's crossbar.
Denayer then produced a brilliant block to deny Mane at the back post following a Henderson corner.
It was frantic entertaining game. The deadlock finally broken in the 75th minute. Liverpool's pressure finally paid off, with sub Origi finding the corner of Pickford's net.
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Hide AdHenderson had played Origi in, he took a touch past Watmore and then curled the ball in, his effort outwitting everyone.
Moyes turned to his subs bench, with Lynden Gooch and Adnan Januzaj brought on for Pienaar and Watmore.
Passions were rising on the touchline too, with Klopp and Paul Bracewell involved in a heated discussion after Firmino went down injured after a firm but fair challenge from Kone.
Liverpool made it 2-0 from the penalty spot in the 90th minute, Milner with the goal after Ndong had clumsily brought down Mane in the area.
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Hide AdSunderland had scrapped hard for 75 minutes but a touch of class from Origi and the late penalty ensured Liverpool took all three points.
Full-time: Liverpool 2 Sunderland 0
Liverpool (4-1-3-2): Karius, Clyne, Matip, Lovren, Milner, Henderson, Can, Wijnaldum (Woodburn, 90), Mane, Coutinho (Origi, 34), Firmino (Lucas, 87)
Subs Not Used: Mignolet, Klavan, Moreno, Ejaria.
Booked: Lovren (67),
Goals: Origi (75), Milner (90).
Sunderland (4-1-4-1): Pickford; Jones, Kone, O'Shea (C), Van Aanholt, Pienaar (Gooch, 79), Denayer, N'Dong, Watmore (Januzaj, 79), Anichebe, Defoe.
Subs Not Used: Mannone, Love, Manquillo, Khazri, Larsson
Booked: Kone (60), O'Shea (64), Pienaar (70),
Goals:
Referee: Anthony Taylor (Greater Manchester)