The hosts dominated possession at Anfield but for a long time it looked as though they would not be able to wear down the Black Cats.
That all changed when Origi squeezed a shot past Jordan Pickford on 75 minutes, with James Milner making sure of the points from the penalty spot in stoppage time.
The big downside for Jurgen Klopp was the sight of Philippe Coutinho going off on a stretcher before half-time, having booted the sole of Lamine Kone's foot.
That just about summed up the first half for Liverpool, who were unable to create their usual raft of chances.
The closest they came before Coutinho's exit was when the Brazilian linked up with Georginio Wijnaldum, but Pickford was on hand to deny the Dutchman on the quarter hour.
Origi was quickly into his stride after coming on and he was fouled by Steven Pienaar, giving Liverpool a free-kick from which they missed the best chance of the opening half.
Jordan Henderson's cross found Dejan Lovren unmarked on 37 minutes, but the defender failed to hit the target with his header.
Eight minutes into the second half Milner came close to scoring the opener.
Emre Can played a beautiful ball over the top for Wijnaldum, who mishit his volley, only to see it work out as a perfect cross for Milner, who was inches from poking the ball into the empty net, as Duncan Watmore desperately tried to cover.
Sunderland had their chance for glory on 71 minutes when Victor Anichebe fed Watmore, but his heavy touch allowed Loris Karius to block it and Liverpool eventually snuffed out the danger.
Two minutes later and Roberto Firmino's fired a low cross towards goal, but neither Origi nor Sadio Mane could apply the finish.
Origi had the answer 60 seconds later. With little on for the Belgian on the edge of the box, he elected to go for a snapshot that crept past Pickford and into the corner of the net.
There was huge relief around Anfield and any surviving nerves were eased in stoppage time when Mane was tripped in the box and Milner slotted home to make sure of the points.