Origi, who replaced midfielder Jordan Henderson on 69 minutes, pounced on following a pass from forward Mohamed Salah to snatch a late win as Liverpool capitalised on Chelsea's 3-2 defeat away to West Ham earlier on Saturday, despite a host of missed chances.
"We came here to win and eventually it happened, that's why we do the hard work in the week for this," a grinning Origi said, adding that manager Jurgen Klopp had sent him on with the instruction: "Be Divock."
The first half was a tense affair, with neither side managing a shot on target, although Salah did find space at the back post after a brilliantly worked move, only to be denied a certain goal by Wolves defender Romain Saiss who intercepted and nicked the ball away.
Liverpool forward Diogo Jota, playing against his former club on his 25th birthday, missed a guilt-edge chance in the second half as stepped past goalkeeper Wolves Jose Sa but could not find a way around opposing defender Conor Coady, who blocked the forward's shot on the goal line. Klopp's side missed another big chance, this time in the dying stages, as forward Sadio Mane failed to score from seven yards out following a deflected header from midfielder Fabinho.
However, replacement Origi struck the ball home from the edge of the six-yard box in the final moments of the match to secure a win for Liverpool, who move to 34 points in the Premier League after 15 games.
Wolves, who have now lost their last 10 Premier League games against Liverpool, sit eighth in the league on 21 points.
"We missed massive chances," Klopp said, reserving a special endorsement for Origi, who features mainly as a substitute given Liverpool's attacking riches.
"Give the ball to Divock was the plan," he said of his late tactical switch. "He's an incredible striker. I love the player. His skills are outstanding. He's one of the best finishers I've seen in my life.
"We played a lot of good stuff. The longer the game goes and it's still nil-nil, you feel the pressure because we wanted the win so badly."